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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

Proof

Step Hyp Ref Expression
1 equequ1 ⊢ z = x → z = y ↔ x = y
2 1 equsalvw ⊢ ∀ z z = x → z = y ↔ x = y