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Theorem mt2 170
Description: A rule similar to modus tollens. (Contributed by NM, 19-Aug-1993.) (Proof shortened by Wolf Lammen, 10-Sep-2013.)
Hypotheses
Ref Expression
mt2.1  |-  ps
mt2.2  |-  ( ph  ->  -.  ps )
Assertion
Ref Expression
mt2  |-  -.  ph

Proof of Theorem mt2
StepHypRef Expression
1 mt2.1 . . 3  |-  ps
21a1i 10 . 2  |-  ( ph  ->  ps )
3 mt2.2 . 2  |-  ( ph  ->  -.  ps )
42, 3pm2.65i 165 1  |-  -.  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4
This theorem is referenced by:  bijust  175  19.2OLD  1686  ax9dgen  1702  elirrv  7327  cardom  7635  0nnn  9793  nthruz  12546  islbs3  15924  hauspwdom  17243  ufinffr  17640  fin1aufil  17643  rectbntr0  18353  i1fd  19052  ex-po  20838  strlem1  22846  nalf  24914  onint1  24960  wlkntrl  28350
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
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