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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  573  en2lp  4272  recnz  8305  fznuz  8931  uznfz  8932
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