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Theorem mt2 190
 Description: A rule similar to modus tollens. Inference associated with con2i 133. (Contributed by NM, 19-Aug-1993.) (Proof shortened by Wolf Lammen, 10-Sep-2013.)
Hypotheses
Ref Expression
mt2.1 𝜓
mt2.2 (𝜑 → ¬ 𝜓)
Assertion
Ref Expression
mt2 ¬ 𝜑

Proof of Theorem mt2
StepHypRef Expression
1 mt2.1 . . 3 𝜓
21a1i 11 . 2 (𝜑𝜓)
3 mt2.2 . 2 (𝜑 → ¬ 𝜓)
42, 3pm2.65i 184 1 ¬ 𝜑
 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  194  ax6dgen  1992  elirrv  8387  cardom  8695  0nnn  10929  nthruz  14820  hauspwdom  21114  fin1aufil  21546  rectbntr0  22443  lgam1  24590  gam1  24591  wlkntrl  26092  ex-po  26684  strlem1  28493  eulerpartlemt  29760  nalf  31572  finxpreclem3  32406  konigsberg-av  41427
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