Is (making) the intention a condition for the validity of prayer? If one performs ablution, can this be (considered) a valid intention?

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.

According to the consensus of scholars, intention is one of the conditions of the validity of prayer. However, ablution alone cannot be deemed a valid intention (for prayer) except if the one who performs the ablution has the intention to offer the prayer to which he performs this ablution from the very beginning of performing it until he recites the Takbeer Al-Ihraam (i.e. the first Takbeer).