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Theorem mt2 179
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 11 . 2  |-  ( ph  ->  ps )
3 mt2.2 . 2  |-  ( ph  ->  -.  ps )
42, 3pm2.65i 173 1  |-  -.  ph
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  bijust  183  ax6dgen  1767  elirrv  7808  cardom  8152  0nnn  10349  nthruz  13530  hauspwdom  19064  fin1aufil  19464  rectbntr0  20368  wlkntrl  23396  ex-po  23577  strlem1  25589  eulerpartlemt  26684  lgam1  26980  gam1  26981  nalf  28179
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