Theorem 3orass 1005

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 1003	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒))
2		orass 772	. 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
3	1, 2	bitri 184	1 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))

Syntax hints:   ↔ wb 105   ∨ wo 713   ∨ w3o 1001

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 714

This theorem depends on definitions:  df-bi 117  df-3or 1003

This theorem is referenced by:  3orrot  1008  3orcomb  1011  3mix1  1190  3bior1fd  1386  sotritric  4415  sotritrieq  4416  ordtriexmid  4613  ontriexmidim  4614  acexmidlemcase  6002  nntri3or  6647  nntri2  6648  exmidontriimlem1  7414  elnnz  9467  elznn0  9472  elznn  9473  zapne  9532  nn01to3  9824  elxr  9984  bezoutlemmain  12535  nninfctlemfo  12577  lgsdilem  15722  gausslemma2dlem4  15759