Theorem alcoms 1469

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

Hypothesis

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

Assertion

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

Proof of Theorem alcoms

Step	Hyp	Ref	Expression
1		ax-7 1441	. 2 |- ( A. y A. x ph -> A. x A. y ph )
2		alcoms.1	. 2 |- ( A. x A. y ph -> ps )
3	1, 2	syl 14	1 |- ( A. y A. x ph -> ps )

Syntax hints:   -> wi 4   A.wal 1346

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-7 1441

This theorem is referenced by:  bj-nfalt  13799