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Theorem pm4.82 868
Description: Theorem *4.82 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.82 (((𝜑𝜓) ∧ (𝜑 → ¬ 𝜓)) ↔ ¬ 𝜑)

Proof of Theorem pm4.82
StepHypRef Expression
1 pm2.65 595 . . 3 ((𝜑𝜓) → ((𝜑 → ¬ 𝜓) → ¬ 𝜑))
21imp 119 . 2 (((𝜑𝜓) ∧ (𝜑 → ¬ 𝜓)) → ¬ 𝜑)
3 pm2.21 557 . . 3 𝜑 → (𝜑𝜓))
4 pm2.21 557 . . 3 𝜑 → (𝜑 → ¬ 𝜓))
53, 4jca 294 . 2 𝜑 → ((𝜑𝜓) ∧ (𝜑 → ¬ 𝜓)))
62, 5impbii 121 1 (((𝜑𝜓) ∧ (𝜑 → ¬ 𝜓)) ↔ ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 101  wb 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
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