As far as Hazrat Abu Bakr (radhiyallahu ‘anhu) is concerned, the bond of love that he enjoyed with Hazrat ‘Ali (radhiyallahu ‘anhu) can be clearly seen from the following incident:

Hazrat Anas (radiyallahu ‘anhu) narrates that Rasulullah (sallallahu ‘alaihi wasallam) was once seated in the Musjid with the Sahaabah (radiyallahu ‘anhum). Hazrat ‘Ali (radiyallahu ‘anhu) then arrived, made salaam, and then remained standing, looking for a place to sit. Rasulullah (sallallahu ‘alaihi wasallam) looked at the faces of the Sahaabah (radiyallahu ‘anhum) to see which of them would make place for him. Hazrat Abu Bakr (radiyallahu ‘anhu), who was seated on the right of Rasulullah (sallallahu ‘alaihi wasallam), immediately moved from his place and said, “Come here, O Abul Hasan.” Hazrat ‘Ali (radiyallahu ‘anhu) then sat in the place of Hazrat Abu Bakr (radhiyallahu ‘anhu), between Rasulullah (sallallahu ‘alaihi wasallam) and Hazrat Abu Bakr (radiyallahu ‘anhu). The Sahaabah (radiyallahu ‘anhum) could actually see the happiness on the blessed face of Rasulullah (sallallahun ‘alaihi wasallam) on account of Hazrat Abu Bakr (radhiyallahu ‘anhu) giving Hazrat ‘Ali (radhiyallahu ‘anhu) his place and honouring him. Rasulullah (sallallahu ‘alaihi wasallam) then turned to Hazrat Abu Bakr (radiyallahu ‘anhu) and said, “O Abu Bakr (radhiyallahu ‘anhu)! It is only people of virtue who recognise the virtue of other people of virtue.” (Bidaayah-wan-Nihaayah 7/358, Maqaasid-ul-Hasanah #212)

In the above incident, we can see that Rasulullah (sallallahu ‘alaihi wasallam) testified to the virtue of both personalities; Hazrat Abu Bakr (radhiyallahu ‘anhu) and Hazrat ‘Ali (radhiyallahu ‘anhu).

As far as Hazrat ‘Umar (radhiyallahu ‘anhu) is concerned, Hazrat ‘Ali (radhiyallahu ‘anhu) got him married to his daughter, Hazrat Ummu Kulthoom (radhiyallahu ‘anha). This is one of the greatest proofs to show the bond of love between Hazrat ‘Ali (radhiyallahu ‘anhu) and Hazrat ‘Umar (radhiyallahu ‘anhu). (Isaabah 8/465)