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Theorem mtpxor 1604
Description: Modus tollendo ponens (original exclusive-or version), aka disjunctive syllogism, similar to mtpor 1603, 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 1603. See rule 3 on [Lopez-Astorga] p. 12 (note that the "or" is the same as mptxor 1602, that is, it is exclusive-or df-xor 1364), 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 1602), 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.)
Ref Expression
Ref Expression

Proof of Theorem mtpxor
StepHypRef Expression
1 mtpxor.min . 2
2 mtpxor.maj . . 3
3 xoror 1370 . . 3
42, 3ax-mp 5 . 2
51, 4mtpor 1603 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  \/wo 368  \/_wxo 1363
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 1364
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