Description: An inference version of the transitive laws for implication luk-1 . Copy of syl with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018) (New usage is discouraged.) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | wl-luk-syl.1 | |- ( ph -> ps ) |
|
| wl-luk-syl.2 | |- ( ps -> ch ) |
||
| Assertion | wl-luk-syl | |- ( ph -> ch ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | wl-luk-syl.1 | |- ( ph -> ps ) |
|
| 2 | wl-luk-syl.2 | |- ( ps -> ch ) |
|
| 3 | 1 | wl-luk-imim1i | |- ( ( ps -> ch ) -> ( ph -> ch ) ) |
| 4 | 2 3 | ax-mp | |- ( ph -> ch ) |