Theorem hbimg 14517

Description: A more general form of hbim 1643.

Hypotheses

Ref	Expression
hbg.1	|- (ph -> A.xps)
hbg.2	|- (ch -> A.xth)

Assertion

Ref	Expression
hbimg	|- ((ps -> ch) -> A.x(ph -> th))

Proof of Theorem hbimg

Step	Hyp	Ref	Expression
1		hbg.1	. . 3 |- (ph -> A.xps)
2	1	ax-gen 1593	. 2 |- A.x(ph -> A.xps)
3		hbg.2	. 2 |- (ch -> A.xth)
4		hbimtg 14514	. 2 |- ((A.x(ph -> A.xps) /\ (ch -> A.xth)) -> ((ps -> ch) -> A.x(ph -> th)))
5	2, 3, 4	mp2an 681	1 |- ((ps -> ch) -> A.x(ph -> th))

Syntax hints:   -> wi 3  A.wal 1584

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 1593  ax-4 1608  ax-5o 1610  ax-6o 1613

This theorem depends on definitions:  df-bi 220  df-an 339

Copyright terms: Public domain