Theorem hbimg 31715

Description: A more general form of hbim 2127. (Contributed by Scott Fenton, 13-Dec-2010.)

Hypotheses

Ref	Expression
hbg.1	|- ( ph -> A. x ps )
hbg.2	|- ( ch -> A. x th )

Assertion

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

Proof of Theorem hbimg

Step	Hyp	Ref	Expression
1		hbg.1	. . 3 |- ( ph -> A. x ps )
2	1	ax-gen 1722	. 2 |- A. x ( ph -> A. x ps )
3		hbg.2	. 2 |- ( ch -> A. x th )
4		hbimtg 31712	. 2 |- ( ( A. x ( ph -> A. x ps ) /\ ( ch -> A. x th ) ) -> ( ( ps -> ch ) -> A. x ( ph -> th ) ) )
5	2, 3, 4	mp2an 708	1 |- ( ( ps -> ch ) -> A. x ( ph -> th ) )

Syntax hints:   -> wi 4   A.wal 1481

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-10 2019  ax-12 2047

This theorem depends on definitions:  df-bi 197  df-an 386  df-ex 1705

This theorem is referenced by: (None)