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Theorem mt4i 153
Description: Modus tollens inference. (Contributed by Wolf Lammen, 12-May-2013.)
Hypotheses
Ref Expression
mt4i.1 𝜒
mt4i.2 (𝜑 → (¬ 𝜓 → ¬ 𝜒))
Assertion
Ref Expression
mt4i (𝜑𝜓)

Proof of Theorem mt4i
StepHypRef Expression
1 mt4i.1 . . 3 𝜒
21a1i 11 . 2 (𝜑𝜒)
3 mt4i.2 . 2 (𝜑 → (¬ 𝜓 → ¬ 𝜒))
42, 3mt4d 152 1 (𝜑𝜓)
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:  0mnnnnn0  11269
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