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Theorem or4 723
Description: Rearrangement of 4 disjuncts. (Contributed by NM, 12-Aug-1994.)
Assertion
Ref Expression
or4 (((𝜑𝜓) ∨ (𝜒𝜃)) ↔ ((𝜑𝜒) ∨ (𝜓𝜃)))

Proof of Theorem or4
StepHypRef Expression
1 or12 718 . . 3 ((𝜓 ∨ (𝜒𝜃)) ↔ (𝜒 ∨ (𝜓𝜃)))
21orbi2i 714 . 2 ((𝜑 ∨ (𝜓 ∨ (𝜒𝜃))) ↔ (𝜑 ∨ (𝜒 ∨ (𝜓𝜃))))
3 orass 719 . 2 (((𝜑𝜓) ∨ (𝜒𝜃)) ↔ (𝜑 ∨ (𝜓 ∨ (𝜒𝜃))))
4 orass 719 . 2 (((𝜑𝜒) ∨ (𝜓𝜃)) ↔ (𝜑 ∨ (𝜒 ∨ (𝜓𝜃))))
52, 3, 43bitr4i 210 1 (((𝜑𝜓) ∨ (𝜒𝜃)) ↔ ((𝜑𝜒) ∨ (𝜓𝜃)))
Colors of variables: wff set class
Syntax hints:  wb 103  wo 664
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  or42  724  orordi  725  orordir  726  3or6  1259  swoer  6300  apcotr  8060
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