Theorem 3orass 937

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 935	. 2 ⊢ ((φ ∨ ψ ∨ χ) ↔ ((φ ∨ ψ) ∨ χ))
2		orass 510	. 2 ⊢ (((φ ∨ ψ) ∨ χ) ↔ (φ ∨ (ψ ∨ χ)))
3	1, 2	bitri 240	1 ⊢ ((φ ∨ ψ ∨ χ) ↔ (φ ∨ (ψ ∨ χ)))

Syntax hints:   ↔ wb 176   ∨ wo 357   ∨ w3o 933

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359  df-3or 935

This theorem is referenced by:  3orrot  940  3orcoma  942  3orcomb  944  3mix1  1124  ecase23d  1285  cador  1391  moeq3  3014  lenltfin  4470