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Theorem mtpxor 1579
 Description: Modus tollendo ponens (original exclusive-or version), aka disjunctive syllogism, similar to mtpor 1578, 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 mtpor 1578. See rule 3 on [Lopez-Astorga] p. 12 (note that the "or" is the same as mptxor 1577, that is, it is exclusive-or df-xor 1352), 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 mptxor 1577), 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.) (Proof shortened by BJ, 19-Apr-2019.)
Hypotheses
Ref Expression
mtpxor.min
mtpxor.maj
Assertion
Ref Expression
mtpxor

Proof of Theorem mtpxor
StepHypRef Expression
1 mtpxor.min . 2
2 mtpxor.maj . . 3
3 xoror 1358 . . 3
42, 3ax-mp 5 . 2
51, 4mtpor 1578 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wo 368   wxo 1351 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-xor 1352 This theorem is referenced by: (None)
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