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  4372  sotritrieq  4373  ordtriexmid  4570  ontriexmidim  4571  acexmidlemcase  5941  nntri3or  6581  nntri2  6582  exmidontriimlem1  7335  elnnz  9384  elznn0  9389  elznn  9390  zapne  9449  nn01to3  9740  elxr  9900  bezoutlemmain  12352  nninfctlemfo  12394  lgsdilem  15537  gausslemma2dlem4  15574