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Theorem orass 739
 Description: Associative law for disjunction. Theorem *4.33 of [WhiteheadRussell] p. 118. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
orass (((𝜑𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))

Proof of Theorem orass
StepHypRef Expression
1 orcom 700 . 2 (((𝜑𝜓) ∨ 𝜒) ↔ (𝜒 ∨ (𝜑𝜓)))
2 or12 738 . 2 ((𝜒 ∨ (𝜑𝜓)) ↔ (𝜑 ∨ (𝜒𝜓)))
3 orcom 700 . . 3 ((𝜒𝜓) ↔ (𝜓𝜒))
43orbi2i 734 . 2 ((𝜑 ∨ (𝜒𝜓)) ↔ (𝜑 ∨ (𝜓𝜒)))
51, 2, 43bitri 205 1 (((𝜑𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
 Colors of variables: wff set class Syntax hints:   ↔ wb 104   ∨ wo 680 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  pm2.31  740  pm2.32  741  or32  742  or4  743  3orass  948  dveeq2  1769  dveeq2or  1770  sbequilem  1792  dvelimALT  1961  dvelimfv  1962  dvelimor  1969  unass  3201  ltxr  9513  lcmass  11673
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