Theorem or32 938

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

Assertion

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

Proof of Theorem or32

Step	Hyp	Ref	Expression
1		orass 934	. 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
2		or12 933	. 2 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) ↔ (𝜓 ∨ (𝜑 ∨ 𝜒)))
3		orcom 883	. 2 ⊢ ((𝜓 ∨ (𝜑 ∨ 𝜒)) ↔ ((𝜑 ∨ 𝜒) ∨ 𝜓))
4	1, 2, 3	3bitri 300	1 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ ((𝜑 ∨ 𝜒) ∨ 𝜓))

Syntax hints:   ↔ wb 209   ∨ wo 860

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 210  df-or 861

This theorem is referenced by:  sspsstri  4062  somo  5598  psslinpr  11004  xrnepnf  13131  xrinfmss  13324  tosso  18461  mulsproplem13  28275  mulsproplem14  28276  satfvsucsuc  35723  lineunray  36505  or32dd  38600