Theorem a7s 1398

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 1392	. 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 1297

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-7 1392

This theorem is referenced by:  cbv2h  1692  hbsb4t  1949  mor  2002