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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 )