Theorem 3orass 948

Description: Associative law for triple disjunction. (Contributed by NM, 8-Apr-1994.)

Assertion

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

Proof of Theorem 3orass

Step	Hyp	Ref	Expression
1		df-3or 946	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒))
2		orass 739	. 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
3	1, 2	bitri 183	1 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))

Syntax hints:   ↔ wb 104   ∨ wo 680   ∨ w3o 944

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681

This theorem depends on definitions:  df-bi 116  df-3or 946

This theorem is referenced by:  3orrot  951  3orcomb  954  3mix1  1133  sotritric  4206  sotritrieq  4207  ordtriexmid  4397  acexmidlemcase  5723  nntri3or  6343  nntri2  6344  elnnz  8968  elznn0  8973  elznn  8974  zapne  9029  nn01to3  9311  elxr  9456  bezoutlemmain  11532