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Theorem mptnan 1683
Description: Modus ponendo tollens 1, one of the "indemonstrables" in Stoic logic. See rule 1 on [Lopez-Astorga] p. 12 , rule 1 on [Sanford] p. 40, and rule A3 in [Hitchcock] p. 5. Sanford describes this rule second (after mptxor 1684) as a "safer, and these days much more common" version of modus ponendo tollens because it avoids confusion between inclusive-or and exclusive-or. (Contributed by David A. Wheeler, 3-Jul-2016.)
Hypotheses
Ref Expression
mptnan.min 𝜑
mptnan.maj ¬ (𝜑𝜓)
Assertion
Ref Expression
mptnan ¬ 𝜓

Proof of Theorem mptnan
StepHypRef Expression
1 mptnan.min . 2 𝜑
2 mptnan.maj . . 3 ¬ (𝜑𝜓)
32imnani 437 . 2 (𝜑 → ¬ 𝜓)
41, 3ax-mp 5 1 ¬ 𝜓
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wa 382
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 195  df-an 384
This theorem is referenced by:  mptxor  1684  alephsucpw2  8692  aleph1re  14680
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