Description: Nested syllogism deduction. Deduction associated with syld . Double deduction associated with syl . (Contributed by NM, 12-Dec-2004) (Proof shortened by Wolf Lammen, 11-May-2013)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | syldd.1 | |- ( ph -> ( ps -> ( ch -> th ) ) ) |
|
| syldd.2 | |- ( ph -> ( ps -> ( th -> ta ) ) ) |
||
| Assertion | syldd | |- ( ph -> ( ps -> ( ch -> ta ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | syldd.1 | |- ( ph -> ( ps -> ( ch -> th ) ) ) |
|
| 2 | syldd.2 | |- ( ph -> ( ps -> ( th -> ta ) ) ) |
|
| 3 | imim2 | |- ( ( th -> ta ) -> ( ( ch -> th ) -> ( ch -> ta ) ) ) |
|
| 4 | 2 1 3 | syl6c | |- ( ph -> ( ps -> ( ch -> ta ) ) ) |