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Theorem mt4 115
Description: The rule of modus tollens. Inference associated with con4i 113. (Contributed by Wolf Lammen, 12-May-2013.)
Hypotheses
Ref Expression
mt4.1 𝜑
mt4.2 𝜓 → ¬ 𝜑)
Assertion
Ref Expression
mt4 𝜓

Proof of Theorem mt4
StepHypRef Expression
1 mt4.1 . 2 𝜑
2 mt4.2 . . 3 𝜓 → ¬ 𝜑)
32con4i 113 . 2 (𝜑𝜓)
41, 3ax-mp 5 1 𝜓
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-3 8
This theorem is referenced by:  infeq5i  8706  chirredi  29562
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