Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. (Contributed by NM, 5-Jan-1993) (Proof shortened by Wolf Lammen, 30-Jul-2012)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | syl6.1 | |- ( ph -> ( ps -> ch ) ) |
|
| syl6.2 | |- ( ch -> th ) |
||
| Assertion | syl6 | |- ( ph -> ( ps -> th ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | syl6.1 | |- ( ph -> ( ps -> ch ) ) |
|
| 2 | syl6.2 | |- ( ch -> th ) |
|
| 3 | 2 | a1i | |- ( ps -> ( ch -> th ) ) |
| 4 | 1 3 | sylcom | |- ( ph -> ( ps -> th ) ) |