Theorem or32 924

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 920	. 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
2		or12 919	. 2 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) ↔ (𝜓 ∨ (𝜑 ∨ 𝜒)))
3		orcom 869	. 2 ⊢ ((𝜓 ∨ (𝜑 ∨ 𝜒)) ↔ ((𝜑 ∨ 𝜒) ∨ 𝜓))
4	1, 2, 3	3bitri 297	1 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ ((𝜑 ∨ 𝜒) ∨ 𝜓))

Syntax hints:   ↔ wb 206   ∨ wo 846

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 207  df-or 847

This theorem is referenced by:  sspsstri  4128  somo  5646  psslinpr  11100  xrnepnf  13181  xrinfmss  13372  tosso  18489  mulsproplem13  28172  mulsproplem14  28173  satfvsucsuc  35333  lineunray  36111  or32dd  38054