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Theorem mt2 183
Description: A rule similar to modus tollens. Inference associated with con2i 124. (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 177 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  187  ax6dgen  1901  elirrv  8109  cardom  8417  0nnn  10638  nthruz  14297  hauspwdom  20509  fin1aufil  20940  rectbntr0  21843  lgam1  23982  gam1  23983  wlkntrl  25285  ex-po  25878  strlem1  27896  eulerpartlemt  29197  nalf  31056  finxpreclem3  31778
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