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Theorem mptnan 1405
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 1406) 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  |-  ph
mptnan.maj  |-  -.  ( ph  /\  ps )
Assertion
Ref Expression
mptnan  |-  -.  ps

Proof of Theorem mptnan
StepHypRef Expression
1 mptnan.min . 2  |-  ph
2 mptnan.maj . . 3  |-  -.  ( ph  /\  ps )
32imnani 681 . 2  |-  ( ph  ->  -.  ps )
41, 3ax-mp 5 1  |-  -.  ps
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  mptxor  1406
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