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Theorem mt2 569
Description: A rule similar to modus tollens. (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 9 . 2 (𝜑𝜓)
3 mt2.2 . 2 (𝜑 → ¬ 𝜓)
42, 3pm2.65i 568 1 ¬ 𝜑
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 544  ax-in2 545
This theorem is referenced by:  0nnn  7917  nn0ge2m1nn  8214
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