Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. (Contributed by NM, 1-Aug-1994) (Proof shortened by Wolf Lammen, 3-Aug-2012)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | syl8.1 | |- ( ph -> ( ps -> ( ch -> th ) ) ) |
|
| syl8.2 | |- ( th -> ta ) |
||
| Assertion | syl8 | |- ( ph -> ( ps -> ( ch -> ta ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | syl8.1 | |- ( ph -> ( ps -> ( ch -> th ) ) ) |
|
| 2 | syl8.2 | |- ( th -> ta ) |
|
| 3 | 2 | a1i | |- ( ph -> ( th -> ta ) ) |
| 4 | 1 3 | syl6d | |- ( ph -> ( ps -> ( ch -> ta ) ) ) |