Metamath Proof Explorer


Theorem eqcoms

Description: Inference applying commutative law for class equality to an antecedent. (Contributed by NM, 24-Jun-1993)

Ref Expression
Hypothesis eqcoms.1 A=Bφ
Assertion eqcoms B=Aφ

Proof

Step Hyp Ref Expression
1 eqcoms.1 A=Bφ
2 eqcom B=AA=B
3 2 1 sylbi B=Aφ