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 )