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Theorem pm5.15 1010
Description: Theorem *5.15 of [WhiteheadRussell] p. 124. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 15-Oct-2013.)
Assertion
Ref Expression
pm5.15 ((𝜑𝜓) ∨ (𝜑 ↔ ¬ 𝜓))

Proof of Theorem pm5.15
StepHypRef Expression
1 xor3 387 . . 3 (¬ (𝜑𝜓) ↔ (𝜑 ↔ ¬ 𝜓))
21biimpi 219 . 2 (¬ (𝜑𝜓) → (𝜑 ↔ ¬ 𝜓))
32orri 859 1 ((𝜑𝜓) ∨ (𝜑 ↔ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 209  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-or 845
This theorem is referenced by:  sbc2or  3756
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