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Theorem dfxor5 37575
Description: Express exclusive-or in terms of implication and negation. Statement in [Frege1879] p. 12. (Contributed by RP, 14-Apr-2020.)
Assertion
Ref Expression
dfxor5 ((𝜑𝜓) ↔ ¬ ((𝜑 → ¬ 𝜓) → ¬ (¬ 𝜑𝜓)))

Proof of Theorem dfxor5
StepHypRef Expression
1 dfxor4 37574 . 2 ((𝜑𝜓) ↔ ¬ ((¬ 𝜑𝜓) → ¬ (𝜑 → ¬ 𝜓)))
2 con2b 349 . 2 (((¬ 𝜑𝜓) → ¬ (𝜑 → ¬ 𝜓)) ↔ ((𝜑 → ¬ 𝜓) → ¬ (¬ 𝜑𝜓)))
31, 2xchbinx 324 1 ((𝜑𝜓) ↔ ¬ ((𝜑 → ¬ 𝜓) → ¬ (¬ 𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wxo 1461
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 385  df-an 386  df-xor 1462
This theorem is referenced by: (None)
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