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Theorem mpto1 1542
 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 1543) 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
mpto1.2
Assertion
Ref Expression
mpto1

Proof of Theorem mpto1
StepHypRef Expression
1 mpto1.1 . 2
2 mpto1.2 . . 3
32imnani 413 . 2
41, 3ax-mp 8 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 359 This theorem is referenced by:  alephsucpw2  7984  aleph1re  12836 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 178  df-an 361
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