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Theorem mptxor 1385
 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, 2-Mar-2018.)
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 . . . 4 (𝜑𝜓)
3 df-xor 1337 . . . 4 ((𝜑𝜓) ↔ ((𝜑𝜓) ∧ ¬ (𝜑𝜓)))
42, 3mpbi 144 . . 3 ((𝜑𝜓) ∧ ¬ (𝜑𝜓))
54simpri 112 . 2 ¬ (𝜑𝜓)
61, 5mptnan 1384 1 ¬ 𝜓
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   ∧ wa 103   ∨ wo 680   ⊻ wxo 1336 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587 This theorem depends on definitions:  df-bi 116  df-xor 1337 This theorem is referenced by: (None)
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