Theorem alcoms

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

	Ref	Expression
Hypothesis	alcoms.1	$$⊢\forall x\forall y\phi \to \psi$$
Assertion	alcoms	$$⊢\forall y\forall x\phi \to \psi$$

Proof

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