Theorem a7s 1735

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

Hypothesis

Ref	Expression
a7s.1	|- (A.xA.yph -> ps)

Assertion

Ref	Expression
a7s	|- (A.yA.xph -> ps)

Proof of Theorem a7s

Step	Hyp	Ref	Expression
1		ax-7 1734	. 2 |- (A.yA.xph -> A.xA.yph)
2		a7s.1	. 2 |- (A.xA.yph -> ps)
3	1, 2	syl 15	1 |- (A.yA.xph -> ps)

Syntax hints:   -> wi 4  A.wal 1540

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-7 1734

This theorem is referenced by:  cbv3hv  1850  cbv3hvOLD  1851  cbv1h  1978  cbv2h  1980  sb9i  2094  ax10-16  2190