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Theorem mt2 202
 Description: A rule similar to modus tollens. Inference associated with con2i 141. (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 196 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  206  ax6dgen  2131  elirrv  9063  cardom  9418  0nnnALT  11677  nthruz  15609  hauspwdom  22112  fin1aufil  22543  rectbntr0  23443  lgam1  25644  gam1  25645  konigsberg  28039  ex-po  28217  strlem1  30030  eulerpartlemt  31633  nalfal  33755  finxpreclem3  34678
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