Description: A syllogism rule of inference. The first premise is used to replace the second antecedent of the second premise. (Contributed by NM, 27-Dec-1992) (Proof shortened by Wolf Lammen, 25-May-2013)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | syl5.1 | |- ( ph -> ps ) |
|
| syl5.2 | |- ( ch -> ( ps -> th ) ) |
||
| Assertion | syl5 | |- ( ch -> ( ph -> th ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | syl5.1 | |- ( ph -> ps ) |
|
| 2 | syl5.2 | |- ( ch -> ( ps -> th ) ) |
|
| 3 | 1 2 | syl5com | |- ( ph -> ( ch -> th ) ) |
| 4 | 3 | com12 | |- ( ch -> ( ph -> th ) ) |