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 )