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Theorem mtand 591
Description: A modus tollens deduction. (Contributed by Jeff Hankins, 19-Aug-2009.)
Hypotheses
Ref Expression
mtand.1 (𝜑 → ¬ 𝜒)
mtand.2 ((𝜑𝜓) → 𝜒)
Assertion
Ref Expression
mtand (𝜑 → ¬ 𝜓)

Proof of Theorem mtand
StepHypRef Expression
1 mtand.1 . 2 (𝜑 → ¬ 𝜒)
2 mtand.2 . . 3 ((𝜑𝜓) → 𝜒)
32ex 108 . 2 (𝜑 → (𝜓𝜒))
41, 3mtod 589 1 (𝜑 → ¬ 𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem is referenced by:  frirrg  4082  phpm  6305  diffisn  6327  addcanprleml  6684  addcanprlemu  6685
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