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Theorem or32 697
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 694 . 2 (((𝜑𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓𝜒)))
2 or12 693 . 2 ((𝜑 ∨ (𝜓𝜒)) ↔ (𝜓 ∨ (𝜑𝜒)))
3 orcom 657 . 2 ((𝜓 ∨ (𝜑𝜒)) ↔ ((𝜑𝜒) ∨ 𝜓))
41, 2, 33bitri 199 1 (((𝜑𝜓) ∨ 𝜒) ↔ ((𝜑𝜒) ∨ 𝜓))
Colors of variables: wff set class
Syntax hints:  wb 102  wo 639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640
This theorem depends on definitions:  df-bi 114
This theorem is referenced by:  xrnepnf  8801
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