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Theorem pm5.62 959
Description: Theorem *5.62 of [WhiteheadRussell] p. 125. (Contributed by Roy F. Longton, 21-Jun-2005.)
Assertion
Ref Expression
pm5.62 (((𝜑𝜓) ∨ ¬ 𝜓) ↔ (𝜑 ∨ ¬ 𝜓))

Proof of Theorem pm5.62
StepHypRef Expression
1 exmid 429 . 2 (𝜓 ∨ ¬ 𝜓)
2 ordir 904 . 2 (((𝜑𝜓) ∨ ¬ 𝜓) ↔ ((𝜑 ∨ ¬ 𝜓) ∧ (𝜓 ∨ ¬ 𝜓)))
31, 2mpbiran2 955 1 (((𝜑𝜓) ∨ ¬ 𝜓) ↔ (𝜑 ∨ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  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: (None)
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