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Theorem pm5.31 571
Description: Theorem *5.31 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.31  |-  ( ( ch  /\  ( ph  ->  ps ) )  -> 
( ph  ->  ( ps 
/\  ch ) ) )

Proof of Theorem pm5.31
StepHypRef Expression
1 pm3.21 435 . . 3  |-  ( ch 
->  ( ps  ->  ( ps  /\  ch ) ) )
21imim2d 48 . 2  |-  ( ch 
->  ( ( ph  ->  ps )  ->  ( ph  ->  ( ps  /\  ch ) ) ) )
32imp 418 1  |-  ( ( ch  /\  ( ph  ->  ps ) )  -> 
( ph  ->  ( ps 
/\  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 358
This theorem is referenced by:  tartarmap  25300
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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