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Theorem pm3.31 432
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 19 . 2  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  ( ph  ->  ( ps  ->  ch ) ) )
21imp3a 420 1  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( ph  /\  ps )  ->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  impexp  433  imp5a  581  issref  5056  ismonc  25814  isepic  25824  stoweidlem17  27766  trsbc  28304  3impexpVD  28632  trsbcVD  28653  19.41rgVD  28678
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
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