Description: A nested syllogism inference with different antecedents. (Contributed by NM, 13-May-1993) (Proof shortened by Josh Purinton, 29-Dec-2000)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | syl9.1 | |- ( ph -> ( ps -> ch ) ) |
|
| syl9.2 | |- ( th -> ( ch -> ta ) ) |
||
| Assertion | syl9 | |- ( ph -> ( th -> ( ps -> ta ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | syl9.1 | |- ( ph -> ( ps -> ch ) ) |
|
| 2 | syl9.2 | |- ( th -> ( ch -> ta ) ) |
|
| 3 | 2 | a1i | |- ( ph -> ( th -> ( ch -> ta ) ) ) |
| 4 | 1 3 | syl5d | |- ( ph -> ( th -> ( ps -> ta ) ) ) |