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Theorem mt2i 583
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 9 . 2 (𝜑𝜒)
3 mt2i.2 . 2 (𝜑 → (𝜓 → ¬ 𝜒))
42, 3mt2d 565 1 (𝜑 → ¬ 𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-in1 554  ax-in2 555
This theorem is referenced by:  0mnnnnn0  8270  climuni  10037
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