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Theorem mt2d 109
Description: Modus tollens deduction. (Contributed by NM, 4-Jul-1994.)
Hypotheses
Ref Expression
mt2d.1 (φχ)
mt2d.2 (φ → (ψ → ¬ χ))
Assertion
Ref Expression
mt2d (φ → ¬ ψ)

Proof of Theorem mt2d
StepHypRef Expression
1 mt2d.1 . 2 (φχ)
2 mt2d.2 . . 3 (φ → (ψ → ¬ χ))
32con2d 107 . 2 (φ → (χ → ¬ ψ))
41, 3mpd 14 1 (φ → ¬ ψ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  mt2i  110  nsyl3  111
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