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 = B → φ
Assertion eqcoms ⊢ B = A → φ

Proof

Step Hyp Ref Expression
1 eqcoms.1 ⊢ A = B → φ
2 eqcom ⊢ B = A ↔ A = B
3 2 1 sylbi ⊢ B = A → φ