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Theorem mtand 590
Description: A modus tollens deduction. (Contributed by Jeff Hankins, 19-Aug-2009.)
Hypotheses
Ref Expression
mtand.1 (φ → ¬ χ)
mtand.2 ((φ ψ) → χ)
Assertion
Ref Expression
mtand (φ → ¬ ψ)

Proof of Theorem mtand
StepHypRef Expression
1 mtand.1 . 2 (φ → ¬ χ)
2 mtand.2 . . 3 ((φ ψ) → χ)
32ex 108 . 2 (φ → (ψχ))
41, 3mtod 588 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:  addcanprleml  6588  addcanprlemu  6589
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