Theorem or12

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

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

Proof

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