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Theorem pm3.37 562
Description: Theorem *3.37 (Transp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 23-Oct-2012.)
Assertion
Ref Expression
pm3.37  |-  ( ( ( ph  /\  ps )  ->  ch )  -> 
( ( ph  /\  -.  ch )  ->  -.  ps ) )

Proof of Theorem pm3.37
StepHypRef Expression
1 pm4.14 561 . 2  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ( ph  /\  -.  ch )  ->  -.  ps ) )
21biimpi 186 1  |-  ( ( ( ph  /\  ps )  ->  ch )  -> 
( ( ph  /\  -.  ch )  ->  -.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 358
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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