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Theorem mpto2 1312
 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
mpto2.1 φ
mpto2.2 (φψ)
Assertion
Ref Expression
mpto2 ¬ ψ

Proof of Theorem mpto2
StepHypRef Expression
1 mpto2.1 . 2 φ
2 mpto2.2 . . . 4 (φψ)
3 df-xor 1266 . . . 4 ((φψ) ↔ ((φ ψ) ¬ (φ ψ)))
42, 3mpbi 133 . . 3 ((φ ψ) ¬ (φ ψ))
54simpri 106 . 2 ¬ (φ ψ)
61, 5mpto1 1311 1 ¬ ψ
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   ∧ wa 97   ∨ wo 628   ⊻ wxo 1265 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545 This theorem depends on definitions:  df-bi 110  df-xor 1266 This theorem is referenced by: (None)
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