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Theorem mt2d 625
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 624 . 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 614  ax-in2 615
This theorem is referenced by:  nsyl3  626  mt2i  644  en2lp  4554  recnz  9346  xnn0dcle  9802  fznuz  10102  uznfz  10103  pcadd  12339  oddennn  12393  lgseisenlem1  14453
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