Theorem hbim1 1103

Description: A closed form of hbim 1007.

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 9	. 2 |- ((ph -> ps) -> (ph -> A.xps))
3		hbim1.1	. . 3 |- (ph -> A.xph)
4	3	19.21 1056	. 2 |- (A.x(ph -> ps) <-> (ph -> A.xps))
5	2, 4	sylibr 200	1 |- ((ph -> ps) -> A.x(ph -> ps))

Syntax hints:   -> wi 3  A.wal 954

This theorem is referenced by:  sbco2d 1256  cbvald 1320  ax15 1359  hbsbc1 1949  reuuni2f 2883

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 963  ax-4 973  ax-5o 975  ax-6o 978

This theorem depends on definitions:  df-bi 147

Copyright terms: Public domain