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Metamath Proof Explorer

Theorem eqvreleqi

Description: Equality theorem for equivalence relation, inference version. (Contributed by Peter Mazsa, 23-Sep-2021)

Ref Expression
Hypothesis eqvreleqi.1 ⊢ R = S
Assertion eqvreleqi ⊢ EqvRel R ↔ EqvRel S

Proof

Step Hyp Ref Expression
1 eqvreleqi.1 ⊢ R = S
2 eqvreleq ⊢ R = S → EqvRel R ↔ EqvRel S
3 1 2 ax-mp ⊢ EqvRel R ↔ EqvRel S