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Theorem hbimg 25437
Description: A more general form of hbim 1836. (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 1555 . 2  |-  A. x
( ph  ->  A. x ps )
3 hbg.2 . 2  |-  ( ch 
->  A. x th )
4 hbimtg 25434 . 2  |-  ( ( A. x ( ph  ->  A. x ps )  /\  ( ch  ->  A. x th ) )  ->  (
( ps  ->  ch )  ->  A. x ( ph  ->  th ) ) )
52, 3, 4mp2an 654 1  |-  ( ( ps  ->  ch )  ->  A. x ( ph  ->  th ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1549
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551
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