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Theorem mpto2 1540
 Description: Modus ponendo tollens 2, one of the "indemonstrables" in Stoic logic. Note that this uses exclusive-or . See rule 2 on [Lopez-Astorga] p. 12 , rule 4 on [Sanford] p. 39 and rule A4 in [Hitchcock] p. 5 . (Contributed by David A. Wheeler, 3-Jul-2016.) (Proof shortened by Wolf Lammen, 12-Nov-2017.)
Hypotheses
Ref Expression
mpto2.1
mpto2.2
Assertion
Ref Expression
mpto2

Proof of Theorem mpto2
StepHypRef Expression
1 mpto2.1 . 2
2 mpto2.2 . . . 4
3 df-xor 1311 . . . 4
42, 3mpbi 200 . . 3
5 xor3 347 . . 3
64, 5mpbi 200 . 2
71, 6mpbi 200 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 177   wxo 1310 This theorem is referenced by:  mtp-xor  1542 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-xor 1311
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