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Metamath Proof Explorer

Theorem alcoms

Description: Swap quantifiers in an antecedent. (Contributed by NM, 11-May-1993)

		Ref	Expression
	Hypothesis	alcoms.1	$⊢ \forall x \forall y φ \to ψ$
	Assertion	alcoms	$⊢ \forall y \forall x φ \to ψ$

Step	Hyp	Ref	Expression
1		alcoms.1	$⊢ \forall x \forall y φ \to ψ$
2		ax-11	$⊢ \forall y \forall x φ \to \forall x \forall y φ$
3	2 1	syl	$⊢ \forall y \forall x φ \to ψ$