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Theorem pm4.83 1021
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 891 . . 3 (𝜑 ∨ ¬ 𝜑)
21a1bi 365 . 2 (𝜓 ↔ ((𝜑 ∨ ¬ 𝜑) → 𝜓))
3 jaob 958 . 2 (((𝜑 ∨ ¬ 𝜑) → 𝜓) ↔ ((𝜑𝜓) ∧ (¬ 𝜑𝜓)))
42, 3bitr2i 278 1 (((𝜑𝜓) ∧ (¬ 𝜑𝜓)) ↔ 𝜓)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 208  wa 398  wo 843
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 209  df-an 399  df-or 844
This theorem is referenced by:  cases2  1042  dmdbr5ati  30184  cvlsupr3  36516  rp-fakeanorass  40014
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