Theorem hbim1 781

Description: A closed form of hbim 702.

Hypotheses

Ref	Expression
hbim1.1	|- (ph -> A.xph)
hbim1.2	|- (ph -> (ps -> A.xps))

Assertion

Ref	Expression
hbim1	|- ((ph -> ps) -> A.x(ph -> ps))

Proof of Theorem hbim1

Step	Hyp	Ref	Expression
1		hbim1.2	. . 3 |- (ph -> (ps -> A.xps))
2	1	a2i 8	. 2 |- ((ph -> ps) -> (ph -> A.xps))
3		hbim1.1	. . 3 |- (ph -> A.xph)
4	3	19.21 738	. 2 |- (A.x(ph -> ps) <-> (ph -> A.xps))
5	2, 4	sylibr 175	1 |- ((ph -> ps) -> A.x(ph -> ps))

Syntax hints:   -> wi 2  A.wal 672

This theorem is referenced by:  sbco2d 914  cbvald 977  ax15 1006  hbsbc 1446

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6  ax-4 673  ax-5 674  ax-6 675  ax-gen 677

This theorem depends on definitions:  df-bi 128

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