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Metamath Proof Explorer

Theorem equcoms

Description: An inference commuting equality in antecedent. Used to eliminate the need for a syllogism. (Contributed by NM, 10-Jan-1993)

		Ref	Expression
	Hypothesis	equcoms.1	$⊢ x = y \to φ$
	Assertion	equcoms	$⊢ y = x \to φ$

Step	Hyp	Ref	Expression
1		equcoms.1	$⊢ x = y \to φ$
2		equcomi	$⊢ y = x \to x = y$
3	2 1	syl	$⊢ y = x \to φ$