Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  hbimg Unicode version

Theorem hbimg 24166
Description: A more general form of hbim 1725. (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
StepHypRef Expression
1 hbg.1 . . 3  |-  ( ph  ->  A. x ps )
21ax-gen 1533 . 2  |-  A. x
( ph  ->  A. x ps )
3 hbg.2 . 2  |-  ( ch 
->  A. x th )
4 hbimtg 24163 . 2  |-  ( ( A. x ( ph  ->  A. x ps )  /\  ( ch  ->  A. x th ) )  ->  (
( ps  ->  ch )  ->  A. x ( ph  ->  th ) ) )
52, 3, 4mp2an 653 1  |-  ( ( ps  ->  ch )  ->  A. x ( ph  ->  th ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177  df-an 360
  Copyright terms: Public domain W3C validator