Description: Associative law for disjunction. Theorem *4.33 of WhiteheadRussell p. 118. (Contributed by NM, 5-Aug-1993) (Proof shortened by Andrew Salmon, 26-Jun-2011)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | orass | |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | orcom | |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ch \/ ( ph \/ ps ) ) ) |
|
| 2 | or12 | |- ( ( ch \/ ( ph \/ ps ) ) <-> ( ph \/ ( ch \/ ps ) ) ) |
|
| 3 | orcom | |- ( ( ch \/ ps ) <-> ( ps \/ ch ) ) |
|
| 4 | 3 | orbi2i | |- ( ( ph \/ ( ch \/ ps ) ) <-> ( ph \/ ( ps \/ ch ) ) ) |
| 5 | 1 2 4 | 3bitri | |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) ) |