Description: Partial elimination of a triple disjunction by denial of a disjunct. (Contributed by Scott Fenton, 26-Mar-2011) (Proof shortened by Andrew Salmon, 25-May-2011)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | 3orel2 | |- ( -. ps -> ( ( ph \/ ps \/ ch ) -> ( ph \/ ch ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 3orrot | |- ( ( ph \/ ps \/ ch ) <-> ( ps \/ ch \/ ph ) ) |
|
| 2 | 3orel1 | |- ( -. ps -> ( ( ps \/ ch \/ ph ) -> ( ch \/ ph ) ) ) |
|
| 3 | orcom | |- ( ( ch \/ ph ) <-> ( ph \/ ch ) ) |
|
| 4 | 2 3 | syl6ib | |- ( -. ps -> ( ( ps \/ ch \/ ph ) -> ( ph \/ ch ) ) ) |
| 5 | 1 4 | syl5bi | |- ( -. ps -> ( ( ph \/ ps \/ ch ) -> ( ph \/ ch ) ) ) |