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Theorem pm4.83 965
Description: Theorem *4.83 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.83 (((𝜑𝜓) ∧ (¬ 𝜑𝜓)) ↔ 𝜓)

Proof of Theorem pm4.83
StepHypRef Expression
1 exmid 429 . . 3 (𝜑 ∨ ¬ 𝜑)
21a1bi 350 . 2 (𝜓 ↔ ((𝜑 ∨ ¬ 𝜑) → 𝜓))
3 jaob 817 . 2 (((𝜑 ∨ ¬ 𝜑) → 𝜓) ↔ ((𝜑𝜓) ∧ (¬ 𝜑𝜓)))
42, 3bitr2i 263 1 (((𝜑𝜓) ∧ (¬ 𝜑𝜓)) ↔ 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 194  wo 381  wa 382
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 195  df-or 383  df-an 384
This theorem is referenced by:  dmdbr5ati  28467  cvlsupr3  33448  rp-fakeanorass  36676
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