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