Metamath Proof Explorer

Theorem equvelv

Description: A biconditional form of equvel with disjoint variable conditions and proved from Tarski's FOL axiom schemes. (Contributed by Andrew Salmon, 2-Jun-2011) Reduce axiom usage. (Revised by Wolf Lammen, 10-Apr-2021) (Proof shortened by Wolf Lammen, 12-Jul-2022)

Ref Expression
Assertion equvelv z z = x z = y x = y


Step Hyp Ref Expression
1 equequ1 z = x z = y x = y
2 1 equsalvw z z = x z = y x = y