Theorem a7s 689

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-7 676	. 2 |- (A.yA.xph -> A.xA.yph)
2		a7s.1	. 2 |- (A.xA.yph -> ps)
3	1, 2	syl 12	1 |- (A.yA.xph -> ps)

Syntax hints:   -> wi 2  A.wal 672

This theorem is referenced by:  cbv1 845  cbv2 846  hbsb4 905  hbsb4t 906  sb9i 920  mo 1020

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-mp 6  ax-7 676

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