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Theorem mtand 637
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 114 . 2 (𝜑 → (𝜓𝜒))
41, 3mtod 635 1 (𝜑 → ¬ 𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 103
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 107  ax-in1 586  ax-in2 587
This theorem is referenced by:  frirrg  4230  phpm  6709  diffisn  6737  tridc  6743  pm54.43  6992  addcanprleml  7363  addcanprlemu  7364  iseqf1olemklt  10144  pw2dvdseulemle  11683  sqne2sq  11693  ctinfomlemom  11778  pwle2  12872  nninfalllemn  12879
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