Theorem or12 949

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		pm1.5 948	. 2 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ (𝜑 ∨ 𝜒)))
2		pm1.5 948	. 2 ⊢ ((𝜓 ∨ (𝜑 ∨ 𝜒)) → (𝜑 ∨ (𝜓 ∨ 𝜒)))
3	1, 2	impbii 201	1 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) ↔ (𝜓 ∨ (𝜑 ∨ 𝜒)))

Syntax hints:   ↔ wb 198   ∨ wo 878

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 199  df-or 879

This theorem is referenced by:  orass  950  or32  954  or4  955  3orcoma  1117  sotrieq  5293  ordzsl  7311  plydivex  24458  nosepon  32352