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Theorem mt2 184
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 178 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  188  ax6dgen  1919  elirrv  8130  cardom  8438  0nnn  10663  nthruz  14381  hauspwdom  20593  fin1aufil  21025  rectbntr0  21928  lgam1  24068  gam1  24069  wlkntrl  25371  ex-po  25964  strlem1  27984  eulerpartlemt  29277  nalf  31134  finxpreclem3  31855  konigsberg-av  40171
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