Y-Δ transform proof using superposition

[Biker]

In the wikipedia page and on every book they proof the transformation by equaling the the equivalent resistance between any pair of terminals while disconnecting the other node.https://en.wikipedia.org/wiki/Y-Δ_transform

Why this should make the two circuits equal? How can we apply superposition here? I have searched everywhere for this answer, In no where anyone explained this. Please explain the principle or this way of proof

 

[anorlunda]

In general, when equations are linear you can apply superposition.

 

[Biker]

In general, when equations are linear you can apply superposition.

Yes I know that but I am asking how you can do that? Like what codition do you put in each situation then sum it up?

In wikipedia they put some conditions on the current in 3 situation but I didnt understand how ?