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Theorem pm3.37 679
Description: Theorem *3.37 (Transp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm3.37  |-  ( ( ( ph  /\  ps )  ->  ch )  -> 
( ( ph  /\  -.  ch )  ->  -.  ps ) )

Proof of Theorem pm3.37
StepHypRef Expression
1 pm3.3 259 . . 3  |-  ( ( ( ph  /\  ps )  ->  ch )  -> 
( ph  ->  ( ps 
->  ch ) ) )
2 con3 632 . . 3  |-  ( ( ps  ->  ch )  ->  ( -.  ch  ->  -. 
ps ) )
31, 2syl6 33 . 2  |-  ( ( ( ph  /\  ps )  ->  ch )  -> 
( ph  ->  ( -. 
ch  ->  -.  ps )
) )
43impd 252 1  |-  ( ( ( ph  /\  ps )  ->  ch )  -> 
( ( ph  /\  -.  ch )  ->  -.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605
This theorem is referenced by:  ndvdssub  11654
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