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Theorem orass 915
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 864 . 2 (((𝜑𝜓) ∨ 𝜒) ↔ (𝜒 ∨ (𝜑𝜓)))
2 or12 914 . 2 ((𝜒 ∨ (𝜑𝜓)) ↔ (𝜑 ∨ (𝜒𝜓)))
3 orcom 864 . . 3 ((𝜒𝜓) ↔ (𝜓𝜒))
43orbi2i 906 . 2 ((𝜑 ∨ (𝜒𝜓)) ↔ (𝜑 ∨ (𝜓𝜒)))
51, 2, 43bitri 298 1 (((𝜑𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
Colors of variables: wff setvar class
Syntax hints:  wb 207  wo 841
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 208  df-or 842
This theorem is referenced by:  pm2.31  916  pm2.32  917  or32  919  or4  920  3orass  1082  axi12  2789  axi12OLD  2790  axbnd  2791  unass  4141  tppreqb  4732  ltxr  12500  lcmass  15948  plydivex  24815  clwwlkneq0  27735  disjxpin  30267  impor  35242  ifpim123g  39746
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