Theorem or32

Description: A rearrangement of disjuncts. (Contributed by NM, 18-Oct-1995) (Proof shortened by Andrew Salmon, 26-Jun-2011)

	Ref	Expression
Assertion	or32	⊢ ( ( ( 𝜑 ∨ 𝜓 ) ∨ 𝜒 ) ↔ ( ( 𝜑 ∨ 𝜒 ) ∨ 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		orass	⊢ ( ( ( 𝜑 ∨ 𝜓 ) ∨ 𝜒 ) ↔ ( 𝜑 ∨ ( 𝜓 ∨ 𝜒 ) ) )
2		or12	⊢ ( ( 𝜑 ∨ ( 𝜓 ∨ 𝜒 ) ) ↔ ( 𝜓 ∨ ( 𝜑 ∨ 𝜒 ) ) )
3		orcom	⊢ ( ( 𝜓 ∨ ( 𝜑 ∨ 𝜒 ) ) ↔ ( ( 𝜑 ∨ 𝜒 ) ∨ 𝜓 ) )
4	1 2 3	3bitri	⊢ ( ( ( 𝜑 ∨ 𝜓 ) ∨ 𝜒 ) ↔ ( ( 𝜑 ∨ 𝜒 ) ∨ 𝜓 ) )