Metamath Proof Explorer


Theorem sbeqal2i

Description: If x = y implies x = z , then we can infer z = y . (Contributed by Andrew Salmon, 3-Jun-2011)

Ref Expression
Hypothesis sbeqal1i.1
|- ( x = y -> x = z )
Assertion sbeqal2i
|- z = y

Proof

Step Hyp Ref Expression
1 sbeqal1i.1
 |-  ( x = y -> x = z )
2 1 sbeqal1i
 |-  y = z
3 2 eqcomi
 |-  z = y