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Theorem mt2i 132
Description: Modus tollens inference. (Contributed by NM, 26-Mar-1995.) (Proof shortened by Wolf Lammen, 15-Sep-2012.)
Hypotheses
Ref Expression
mt2i.1 𝜒
mt2i.2 (𝜑 → (𝜓 → ¬ 𝜒))
Assertion
Ref Expression
mt2i (𝜑 → ¬ 𝜓)

Proof of Theorem mt2i
StepHypRef Expression
1 mt2i.1 . . 3 𝜒
21a1i 11 . 2 (𝜑𝜒)
3 mt2i.2 . 2 (𝜑 → (𝜓 → ¬ 𝜒))
42, 3mt2d 131 1 (𝜑 → ¬ 𝜓)
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:  ssnlim  7031  elirrv  8449  konigthlem  9335  ipo0  38121  ifr0  38122
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