Theorem alcoms

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

	Ref	Expression
Hypothesis	alcoms.1	|- ( A. x A. y ph -> ps )
Assertion	alcoms	|- ( A. y A. x ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		alcoms.1	|- ( A. x A. y ph -> ps )
2		ax-11	|- ( A. y A. x ph -> A. x A. y ph )
3	2 1	syl	|- ( A. y A. x ph -> ps )