Metamath Proof Explorer


Theorem eqeq1i

Description: Inference from equality to equivalence of equalities. (Contributed by NM, 15-Jul-1993)

Ref Expression
Hypothesis eqeq1i.1 A = B
Assertion eqeq1i A = C B = C

Proof

Step Hyp Ref Expression
1 eqeq1i.1 A = B
2 eqeq1 A = B A = C B = C
3 1 2 ax-mp A = C B = C