Theorem a7s 1454

Description: Swap quantifiers in an antecedent. (Contributed by NM, 5-Aug-1993.)

Hypothesis

Ref	Expression
a7s.1	|- ( A. x A. y ph -> ps )

Assertion

Ref	Expression
a7s	|- ( A. y A. x ph -> ps )

Proof of Theorem a7s

Step	Hyp	Ref	Expression
1		ax-7 1448	. 2 |- ( A. y A. x ph -> A. x A. y ph )
2		a7s.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 1351

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-7 1448

This theorem is referenced by:  cbv2h  1748  hbsb4t  2013  mor  2068