Hadith no. 2630 (below) is a repeat. Read it here.
Volume 4, Book 52, Number 234 :
Narrated by Anas (radiallaahu `anhu)
The Prophet (sallallaahu `alayhi wasallam) reached Khaibar in the morning, while the people were coming out carrying their spades over their shoulders. When they saw him they said, “This is Muhammad and his army! Muhammad and his army!” So, they took refuge in the fort. The Prophet (sallallaahu `alayhi wasallam) raised both his hands and said, “Allahu Akbar, Khaibar is ruined, for when we approach a nation (i.e. enemy to fight) then miserable is the morning of the warned ones.” Then we found some donkeys which we (killed and) cooked: The announcer of the Prophet (sallallaahu `alayhi wasallam) announced: “Allah and His Apostle forbid you to eat donkey’s meat.” So, all the pots including their contents were turned upside down.
Volume 4, Book 52, Number 235 :
Narrated by Abu Musa Al-Ashari (radiallaahu `anhu)
We were in the company of Allah’s Apostle (sallallaahu `alayhi wasallam) (during Hajj). Whenever we went up a high place we used to say: “None has the right to be worshipped but Allah, and Allah is Greater,” and our voices used to rise, so the Prophet (sallallaahu `alayhi wasallam) said, “O people! Be merciful to yourselves (i.e. don’t raise your voice), for you are not calling a deaf or an absent one, but One Who is with you, no doubt He is All-Hearer, ever Near (to all things).”
Shaykh al-Islam (may Allah have mercy on him) was asked about a man who established a waqf and in some of his conditions he stipulated that they should recite whatever they are able to (of Qur’aan) and recite Subhaan Allah (Glory be to Allah), Laa ilaaha ill-Allah (there is no God but Allah) and Allahu akbar(Allah is most great), and send blessings upon the Prophet (blessings and peace of Allah be upon him) after Fajr until sunrise. Is it better to do that out loud or quietly?
Praise be to Allah. Rather it is better to recite dhikr and du‘aa’ – such as sending blessings upon the Prophet (blessings and peace of Allah be upon him) – quietly, unless there is a reason to do otherwise. At this particular time it is especially preferable (to recite it quietly), because Allah says (interpretation of the meaning): “And remember your Lord by your tongue and within yourself, humbly and with fear without loudness in words in the mornings” [al-A‘raaf 7:205]. And in as-Saheeh it is narrated from the Prophet (blessings and peace of Allah be upon him) that when he saw the Sahaabah (may Allah be pleased with them) raising their voices in dhikr, he said:
End quote from al-Fataawa al-Kubra, 4/246
Volume 4, Book 52, Number 236 :
Narrated by Jabir bin ‘Abdullah (radiallaahu `anhu)
Whenever we went up a place we would say, “Allahu Akbar (i.e. Allah is Greater)”, and whenever we went down a place we would say, “Subhan Allah.”
Volume 4, Book 52, Number 237 :
Narrated by Jabir (radiallaahu `anhu)
Whenever we went up a place we would say Takbir, and whenever we went down we would say, “Subhan Allah.”
Volume 4, Book 52, Number 238 :
Narrated by Abdullah bin Umar (radiallaahu `anhu)
Whenever the Prophet (sallallaahu `alayhi wasallam) returned from the Hajj or the ‘Umra or a Ghazwa, he would say Takbir thrice. Whenever he came upon a mountain path or wasteland, and then he would say, “None has the right to be worshipped but Allah, Alone Who has no partner. All the Kingdom belongs to Him and all the praises are for Him and He is Omnipotent. We are returning with repentance, worshipping, prostrating ourselves and praising our Lord. Allah fulfilled His Promise, granted victory to His slave and He Alone defeated all the clans.”
Abu Dawood narrated that Ibn ‘Umar taught him that when the Messenger of Allah (blessings and peace of Allah be upon him) got up on his camel, when he was setting out on a journey, he would say takbeer three times, then he would say: “Subhaan allathi sakhkhara lana hadha wa ma kunna lahu muqrineen wa inna ila rabbina la munqaliboon. Allaahumma inna nas’aluka fi safarina haadha al-birra wa’l-taqwa wa min al-‘aml ma tarda, Allaahumma hawwin ‘alayna safarana haadha watwi ‘anna bu’dahu. Allaahumma anta al-saahib fi’l-safar wa’l-khaleefah fi’l-ahl (Glory be to the One Who has placed this (transport) at our service and we ourselves would not have been capable of that, and to our Lord is our final destiny. O Allah, we ask You for righteousness and piety in this journey of ours, and we ask You for deeds which please You. O Allah, facilitate our journey and let us cover its distance quickly. O Allah, You are the Companion on the journey and the Successor (the One Who guards them in a person’s absence) over the family).”
And when he returned he would say the same words and would add to them: “Ayiboona taiboona ‘abidoona li rabbina hamidoon (Returning, repenting, worshipping and praising our Lord).”
When the Prophet (blessings and peace of Allah be upon him) and his army climbed a hill they would say takbeer and when they went downhill they would say tasbeeh.
Those scholars who say that this is mustahabb (recommended) when going up the stairs and so on, say that one should say takbeer when going up and that going up stairs or hills is the same thing.
But others say that saying takbeer when going up the stairs and so on is not prescribed, because that was not narrated except in specific circumstances, namely climbing up a mountain and the like when travelling; with regard to going up the stairs and so on, there is no such report, even though this was something known among them and they used to do it (i.e., climb up and down stairs etc). If it were prescribed, the Prophet (blessings and peace of Allah be upon him) would have done it or he would have taught it to his companions as he taught them what to say when entering the house and when leaving it, and other adhkar (words of remembrance) to be recited every day and night.
This is the most correct view concerning this issue.
Shaykh Ibn ‘Uthaymeen (may Allah have mercy on him) was asked the following question: It says in the hadeeth that the Prophet (blessings and peace of Allah be upon him) used to say takbeer when climbing a hill and tasbeeh when going down into a valley. Is this takbeer and tasbeeh only when travelling, or did he say takbeer – for example – at home when going up to the second and third floor? May Allah reward you with good.
During his journeys, when the Prophet (blessings and peace of Allah be upon him) climbed up a hill he would say takbeer, and when he went down into a valley he would say tasbeeh. That is because the one who is above a thing may feel proud and think that he is great, so it is appropriate for him to proclaim the greatness of Allah, may He be glorified and exalted, by saying: Allahu akbar. And when he descends, he is going down to a lower level, so it is appropriate for him to glorify Allah, may He be glorified and exalted, when going down. This is the context of saying takbeer and tasbeeh.
But there is no report in the Sunnah (prophetic teachings) about doing that when not travelling. Acts of worship are based on tawqeef i.e., they are limited to what is narrated in sound reports. Based on that, when a person goes up the stairs in his house he does not have to say takbeer, and when he comes downstairs he does not have to say tasbeeh. Rather that only applies in the case of travelling.
End quote from Liqaa’aat al-Baab al-Maftooh.
And Allah knows best.
I personally incline towards the first opinion. My two cents about the latter: if the same reasoning is applied to stairs in one’s house, especially if one lives in a tall building and going up and down the elevator/stairs 20-50 floors is a norm, then it is very likely that pride and greatness are felt. Saying Allahu Akbar when going up could humble the person. So to be safe, one could say Takbeer and Tasbeeh not to follow this specific Sunnah but to remember Allah as it is appropriate to remember Him in that situation. Yes?