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Theorem mtp-xor 1545
 Description: Modus tollendo ponens (original exclusive-or version), aka disjunctive syllogism, one of the five "indemonstrables" in Stoic logic. The rule says, "if is not true, and either or (exclusively) are true, then must be true." Today the name "modus tollendo ponens" often refers to a variant, the inclusive-or version as defined in mtp-or 1547. See rule 3 on [Lopez-Astorga] p. 12 (note that the "or" is the same as mpto2 1543, that is, it is exclusive-or df-xor 1314), rule 3 of [Sanford] p. 39 (where it is not as clearly stated which kind of "or" is used but it appears to be in the same sense as mpto2 1543), and rule A5 in [Hitchcock] p. 5 (exclusive-or is expressly used). (Contributed by David A. Wheeler, 4-Jul-2016.) (Proof shortened by Wolf Lammen, 11-Nov-2017.)
Hypotheses
Ref Expression
mtp-xor.1
mtp-xor.2
Assertion
Ref Expression
mtp-xor

Proof of Theorem mtp-xor
StepHypRef Expression
1 mtp-xor.1 . . 3
2 mtp-xor.2 . . . 4
3 xorneg 1322 . . . 4
42, 3mpbir 201 . . 3
51, 4mpto2 1543 . 2
65notnotri 108 1
 Colors of variables: wff set class Syntax hints:   wn 3   wxo 1313 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 1314
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