Theorem or12 920

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		pm1.5 919	. 2 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ (𝜑 ∨ 𝜒)))
2		pm1.5 919	. 2 ⊢ ((𝜓 ∨ (𝜑 ∨ 𝜒)) → (𝜑 ∨ (𝜓 ∨ 𝜒)))
3	1, 2	impbii 209	1 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) ↔ (𝜓 ∨ (𝜑 ∨ 𝜒)))

Syntax hints:   ↔ wb 206   ∨ wo 847

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 207  df-or 848

This theorem is referenced by:  orass  921  or32  925  or4  926  3orcoma  1092  sotrieq  5592  ordzsl  7840  plydivex  26257  nosepon  27629