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Theorem mtand 654
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 114 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
41, 3mtod 652 1  |-  ( ph  ->  -.  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-ia3 107  ax-in1 603  ax-in2 604
This theorem is referenced by:  frirrg  4272  phpm  6759  diffisn  6787  tridc  6793  pm54.43  7046  addcanprleml  7429  addcanprlemu  7430  iseqf1olemklt  10265  pw2dvdseulemle  11852  sqne2sq  11862  ctinfomlemom  11947  ivthinc  12800  pwle2  13223  nninfalllemn  13232
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