Theorem 3orass 983

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 981	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒))
2		orass 768	. 2 ⊢ (((𝜑 ∨ 𝜓) ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))
3	1, 2	bitri 184	1 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ (𝜑 ∨ (𝜓 ∨ 𝜒)))

Syntax hints:   ↔ wb 105   ∨ wo 709   ∨ w3o 979

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 710

This theorem depends on definitions:  df-bi 117  df-3or 981

This theorem is referenced by:  3orrot  986  3orcomb  989  3mix1  1168  sotritric  4355  sotritrieq  4356  ordtriexmid  4553  ontriexmidim  4554  acexmidlemcase  5913  nntri3or  6546  nntri2  6547  exmidontriimlem1  7281  elnnz  9327  elznn0  9332  elznn  9333  zapne  9391  nn01to3  9682  elxr  9842  bezoutlemmain  12135  nninfctlemfo  12177  lgsdilem  15143  gausslemma2dlem4  15180