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Theorem mt2 192
Description: A rule similar to modus tollens. Inference associated with con2i 137. (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 186 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:  bijust0  196  ax6dgen  2179  elirrv  8777  cardom  9132  0nnnALT  11395  nthruz  15363  hauspwdom  21682  fin1aufil  22113  rectbntr0  23012  lgam1  25210  gam1  25211  konigsberg  27632  ex-po  27846  strlem1  29660  eulerpartlemt  30974  nalfal  32931  finxpreclem3  33770
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