Theorem or12 917

Description: Swap two disjuncts. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 14-Nov-2012.)

Assertion

Ref	Expression
or12	⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) ↔ (𝜓 ∨ (𝜑 ∨ 𝜒)))

Proof of Theorem or12

Step	Hyp	Ref	Expression
1		pm1.5 916	. 2 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ (𝜑 ∨ 𝜒)))
2		pm1.5 916	. 2 ⊢ ((𝜓 ∨ (𝜑 ∨ 𝜒)) → (𝜑 ∨ (𝜓 ∨ 𝜒)))
3	1, 2	impbii 208	1 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) ↔ (𝜓 ∨ (𝜑 ∨ 𝜒)))

Syntax hints:   ↔ wb 205   ∨ wo 844

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 206  df-or 845

This theorem is referenced by:  orass  918  or32  922  or4  923  3orcoma  1090  sotrieq  5608  ordzsl  7828  plydivex  26153  nosepon  27517