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Theorem mptxor 1734
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.) (Proof shortened by BJ, 19-Apr-2019.)
Hypotheses
Ref Expression
mptxor.min 𝜑
mptxor.maj (𝜑𝜓)
Assertion
Ref Expression
mptxor ¬ 𝜓

Proof of Theorem mptxor
StepHypRef Expression
1 mptxor.min . 2 𝜑
2 mptxor.maj . . 3 (𝜑𝜓)
3 xornan 1512 . . 3 ((𝜑𝜓) → ¬ (𝜑𝜓))
42, 3ax-mp 5 . 2 ¬ (𝜑𝜓)
51, 4mptnan 1733 1 ¬ 𝜓
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wa 383  wxo 1504
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 197  df-or 384  df-an 385  df-xor 1505
This theorem is referenced by: (None)
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