Theorem a7s 991

Description: Swap quantifiers in an antecedent.

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-7 962	. 2 |- (A.yA.xph -> A.xA.yph)
2		a7s.1	. 2 |- (A.xA.yph -> ps)
3	1, 2	syl 10	1 |- (A.yA.xph -> ps)

Syntax hints:   -> wi 3  A.wal 954

This theorem is referenced by:  cbv1 1162  cbv2 1163  hbsb4 1248  hbsb4t 1249  sb9i 1263  mo 1393  hbfvd2 3731

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-mp 7  ax-7 962

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