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Theorem mt2 191
 Description: A rule similar to modus tollens. Inference associated with con2i 134. (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 185 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  195  ax6dgen  2045  elirrv  8542  cardom  8850  0nnn  11090  nthruz  15026  hauspwdom  21352  fin1aufil  21783  rectbntr0  22682  lgam1  24835  gam1  24836  konigsberg  27235  ex-po  27422  strlem1  29237  eulerpartlemt  30561  nalf  32527  finxpreclem3  33360
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