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Theorem mt2d 599
Description: Modus tollens deduction. (Contributed by NM, 4-Jul-1994.)
Hypotheses
Ref Expression
mt2d.1  |-  ( ph  ->  ch )
mt2d.2  |-  ( ph  ->  ( ps  ->  -.  ch ) )
Assertion
Ref Expression
mt2d  |-  ( ph  ->  -.  ps )

Proof of Theorem mt2d
StepHypRef Expression
1 mt2d.1 . 2  |-  ( ph  ->  ch )
2 mt2d.2 . . 3  |-  ( ph  ->  ( ps  ->  -.  ch ) )
32con2d 598 . 2  |-  ( ph  ->  ( ch  ->  -.  ps ) )
41, 3mpd 13 1  |-  ( ph  ->  -.  ps )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 588  ax-in2 589
This theorem is referenced by:  nsyl3  600  mt2i  618  en2lp  4439  recnz  9112  fznuz  9850  uznfz  9851  oddennn  11832
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