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Theorem mpto1 1528
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 1529) 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  |-  ph
mpto1.2  |-  -.  ( ph  /\  ps )
Assertion
Ref Expression
mpto1  |-  -.  ps

Proof of Theorem mpto1
StepHypRef Expression
1 mpto1.1 . 2  |-  ph
2 mpto1.2 . . 3  |-  -.  ( ph  /\  ps )
32imnani 414 . 2  |-  ( ph  ->  -.  ps )
41, 3ax-mp 10 1  |-  -.  ps
Colors of variables: wff set class
Syntax hints:   -. wn 5    /\ wa 360
This theorem is referenced by:  alephsucpw2  7671  aleph1re  12450
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-an 362
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