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Theorem pm3.31 434
Description: Theorem *3.31 (Imp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 24-Mar-2013.)
Assertion
Ref Expression
pm3.31  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( ph  /\  ps )  ->  ch ) )

Proof of Theorem pm3.31
StepHypRef Expression
1 id 21 . 2  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( ph  ->  ( ps  ->  ch ) ) )
21imp3a 422 1  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( ph  /\  ps )  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    /\ wa 360
This theorem is referenced by:  impexp  435  imp5a  584  issref  4963  ismonc  24980  isepic  24990  trsbc  26997  3impexpVD  27322  trsbcVD  27343  19.41rgVD  27368
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362
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