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Theorem mt2d 555
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 554 . 2 (φ → (χ → ¬ ψ))
41, 3mpd 13 1 (φ → ¬ ψ)
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:  nsyl3  556  mt2i  572  en2lp  4232  recnz  8069  fznuz  8694  uznfz  8695
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