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Theorem mtand 601
Description: A modus tollens deduction. (Contributed by Jeff Hankins, 19-Aug-2009.)
Hypotheses
Ref Expression
mtand.1  |-  ( ph  ->  -.  ch )
mtand.2  |-  ( (
ph  /\  ps )  ->  ch )
Assertion
Ref Expression
mtand  |-  ( ph  ->  -.  ps )

Proof of Theorem mtand
StepHypRef Expression
1 mtand.1 . 2  |-  ( ph  ->  -.  ch )
2 mtand.2 . . 3  |-  ( (
ph  /\  ps )  ->  ch )
32ex 112 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
41, 3mtod 599 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem is referenced by:  frirrg  4115  phpm  6358  diffisn  6381  addcanprleml  6770  addcanprlemu  6771  pw2dvdseulemle  10255
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