Description: A syllogism rule of inference. The first premise is used to replace the third antecedent of the second premise. (Contributed by NM, 12-Jan-1993) (Proof shortened by Wolf Lammen, 3-Aug-2012)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | syl7.1 | |- ( ph -> ps ) |
|
| syl7.2 | |- ( ch -> ( th -> ( ps -> ta ) ) ) |
||
| Assertion | syl7 | |- ( ch -> ( th -> ( ph -> ta ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | syl7.1 | |- ( ph -> ps ) |
|
| 2 | syl7.2 | |- ( ch -> ( th -> ( ps -> ta ) ) ) |
|
| 3 | 1 | a1i | |- ( ch -> ( ph -> ps ) ) |
| 4 | 3 2 | syl5d | |- ( ch -> ( th -> ( ph -> ta ) ) ) |