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Theorem pm5.63 961
Description: Theorem *5.63 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 25-Dec-2012.)
Assertion
Ref Expression
pm5.63 ((𝜑𝜓) ↔ (𝜑 ∨ (¬ 𝜑𝜓)))

Proof of Theorem pm5.63
StepHypRef Expression
1 exmid 430 . . 3 (𝜑 ∨ ¬ 𝜑)
2 ordi 904 . . 3 ((𝜑 ∨ (¬ 𝜑𝜓)) ↔ ((𝜑 ∨ ¬ 𝜑) ∧ (𝜑𝜓)))
31, 2mpbiran 955 . 2 ((𝜑 ∨ (¬ 𝜑𝜓)) ↔ (𝜑𝜓))
43bicomi 213 1 ((𝜑𝜓) ↔ (𝜑 ∨ (¬ 𝜑𝜓)))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 195  wo 382  wa 383
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 196  df-or 384  df-an 385
This theorem is referenced by:  jaoi2  1002  plydivex  23801  lineunray  31218
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