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Theorem pm4.43 1020
Description: Theorem *4.43 of [WhiteheadRussell] p. 119. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 26-Nov-2012.)
Assertion
Ref Expression
pm4.43 (𝜑 ↔ ((𝜑𝜓) ∧ (𝜑 ∨ ¬ 𝜓)))

Proof of Theorem pm4.43
StepHypRef Expression
1 pm3.24 406 . . 3 ¬ (𝜓 ∧ ¬ 𝜓)
21biorfi 936 . 2 (𝜑 ↔ (𝜑 ∨ (𝜓 ∧ ¬ 𝜓)))
3 ordi 1003 . 2 ((𝜑 ∨ (𝜓 ∧ ¬ 𝜓)) ↔ ((𝜑𝜓) ∧ (𝜑 ∨ ¬ 𝜓)))
42, 3bitri 278 1 (𝜑 ↔ ((𝜑𝜓) ∧ (𝜑 ∨ ¬ 𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 209  wa 399  wo 844
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 210  df-an 400  df-or 845
This theorem is referenced by:  stoweidlem26  42594
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