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  4419  sotritrieq  4420  ordtriexmid  4617  ontriexmidim  4618  acexmidlemcase  6008  nntri3or  6656  nntri2  6657  exmidontriimlem1  7426  elnnz  9479  elznn0  9484  elznn  9485  zapne  9544  nn01to3  9841  elxr  10001  bezoutlemmain  12559  nninfctlemfo  12601  lgsdilem  15746  gausslemma2dlem4  15783