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Theorem or32 550
 Description: A rearrangement of disjuncts. (Contributed by NM, 18-Oct-1995.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
or32 (((𝜑𝜓) ∨ 𝜒) ↔ ((𝜑𝜒) ∨ 𝜓))

Proof of Theorem or32
StepHypRef Expression
1 orass 547 . 2 (((𝜑𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
2 or12 546 . 2 ((𝜑 ∨ (𝜓𝜒)) ↔ (𝜓 ∨ (𝜑𝜒)))
3 orcom 401 . 2 ((𝜓 ∨ (𝜑𝜒)) ↔ ((𝜑𝜒) ∨ 𝜓))
41, 2, 33bitri 286 1 (((𝜑𝜓) ∨ 𝜒) ↔ ((𝜑𝜒) ∨ 𝜓))
 Colors of variables: wff setvar class Syntax hints:   ↔ wb 196   ∨ wo 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 197  df-or 384 This theorem is referenced by:  sspsstri  3816  somo  5173  ordtri3OLD  5873  psslinpr  9966  xrnepnf  12066  xrinfmss  12254  tosso  17158  lineunray  32481  or32dd  34128
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