Theorem 3orcomb 1048

Description: Commutation law for triple disjunction. (Contributed by Scott Fenton, 20-Apr-2011.)

Assertion

Ref	Expression
3orcomb	⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓))

Proof of Theorem 3orcomb

Step	Hyp	Ref	Expression
1		orcom 402	. . 3 ⊢ ((𝜓 ∨ 𝜒) ↔ (𝜒 ∨ 𝜓))
2	1	orbi2i 541	. 2 ⊢ ((𝜑 ∨ (𝜓 ∨ 𝜒)) ↔ (𝜑 ∨ (𝜒 ∨ 𝜓)))
3		3orass 1040	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
4		3orass 1040	. 2 ⊢ ((𝜑 ∨ 𝜒 ∨ 𝜓) ↔ (𝜑 ∨ (𝜒 ∨ 𝜓)))
5	2, 3, 4	3bitr4i 292	1 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ 𝜒 ∨ 𝜓))

Syntax hints:   ↔ wb 196   ∨ wo 383   ∨ w3o 1036

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 197  df-or 385  df-3or 1038

This theorem is referenced by:  eueq3  3381  swoso  7775  swrdnd  13432  colcom  25453  legso  25494  lncom  25517  soseq  31751  colinearperm1  32169  frege129d  38055  ordelordALT  38747  ordelordALTVD  39103