Theorem 3orass 984

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 982	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒))
2		orass 769	. 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
3	1, 2	bitri 184	1 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))

Syntax hints:   ↔ wb 105   ∨ wo 710   ∨ w3o 980

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 711

This theorem depends on definitions:  df-bi 117  df-3or 982

This theorem is referenced by:  3orrot  987  3orcomb  990  3mix1  1169  3bior1fd  1364  sotritric  4389  sotritrieq  4390  ordtriexmid  4587  ontriexmidim  4588  acexmidlemcase  5962  nntri3or  6602  nntri2  6603  exmidontriimlem1  7364  elnnz  9417  elznn0  9422  elznn  9423  zapne  9482  nn01to3  9773  elxr  9933  bezoutlemmain  12434  nninfctlemfo  12476  lgsdilem  15619  gausslemma2dlem4  15656