Theorem or12 683

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		pm1.5 682	. 2 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) → (𝜓 ∨ (𝜑 ∨ 𝜒)))
2		pm1.5 682	. 2 ⊢ ((𝜓 ∨ (𝜑 ∨ 𝜒)) → (𝜑 ∨ (𝜓 ∨ 𝜒)))
3	1, 2	impbii 117	1 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) ↔ (𝜓 ∨ (𝜑 ∨ 𝜒)))

Syntax hints:   ↔ wb 98   ∨ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  orass  684  or32  687  or4  688