![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > 3orass | GIF version |
Description: Associative law for triple disjunction. (Contributed by NM, 8-Apr-1994.) |
Ref | Expression |
---|---|
3orass | ⊢ ((φ ∨ ψ ∨ χ) ↔ (φ ∨ (ψ ∨ χ))) |
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))) |
Colors of variables: wff set class |
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 |
Copyright terms: Public domain | W3C validator |