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Theorem mpto1 1533
 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 mpto2 1534) 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
mpto1.1 φ
mpto1.2 ¬ (φ ψ)
Assertion
Ref Expression
mpto1 ¬ ψ

Proof of Theorem mpto1
StepHypRef Expression
1 mpto1.1 . 2 φ
2 mpto1.2 . . 3 ¬ (φ ψ)
32imnani 412 . 2 (φ → ¬ ψ)
41, 3ax-mp 8 1 ¬ ψ
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ∧ wa 358 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 177  df-an 360 This theorem is referenced by: (None)
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