Theorem a7s 967

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-7 954	. 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 950

This theorem is referenced by:  cbv1 1145  cbv2 1146  hbsb4 1232  hbsb4t 1233  sb9i 1247  mo 1370  hbfvd2 3670

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-mp 7  ax-7 954

Copyright terms: Public domain