Theorem hbim1 1458

Description: A closed form of hbim 1354.

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 10	. 2 |- ((ph -> ps) -> (ph -> A.xps))
3		hbim1.1	. . 3 |- (ph -> A.xph)
4	3	19.21 1403	. 2 |- (A.x(ph -> ps) <-> (ph -> A.xps))
5	2, 4	sylibr 217	1 |- ((ph -> ps) -> A.x(ph -> ps))

Syntax hints:   -> wi 3  A.wal 1296

This theorem is referenced by:  sbco2d 1630  cbvaldOLD 1703  ax15 1750  hbsbc1 2462  hbsbc1OLD 2463  reuuni2f 3810  reiota2f 5109  ax12 16367

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1305  ax-4 1319  ax-5o 1321  ax-6o 1324

This theorem depends on definitions:  df-bi 164

Copyright terms: Public domain