Theorem 3orass 887

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 885	. 2 ⊢ ((φ ∨ ψ ∨ χ) ↔ ((φ ∨ ψ) ∨ χ))
2		orass 683	. 2 ⊢ (((φ ∨ ψ) ∨ χ) ↔ (φ ∨ (ψ ∨ χ)))
3	1, 2	bitri 173	1 ⊢ ((φ ∨ ψ ∨ χ) ↔ (φ ∨ (ψ ∨ χ)))

Syntax hints:   ↔ wb 98   ∨ wo 628   ∨ w3o 883

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629

This theorem depends on definitions:  df-bi 110  df-3or 885

This theorem is referenced by:  3orrot  890  3orcomb  893  3mix1  1072  sotritric  4052  sotritrieq  4053  ordtriexmid  4210  acexmidlemcase  5450  nntri3or  6011  nntri2  6012  elnnz  8031  elznn0  8036  elznn  8037  zapne  8091  nn01to3  8328  elxr  8466