Description: A syllogism rule of inference. The second premise is used to replace the consequent of the first premise. Copy of syl6 with a different proof. (Contributed by Wolf Lammen, 17-Dec-2018) (New usage is discouraged.) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | wl-luk-imtrdi.1 | |- ( ph -> ( ps -> ch ) ) |
|
| wl-luk-imtrdi.2 | |- ( ch -> th ) |
||
| Assertion | wl-luk-imtrdi | |- ( ph -> ( ps -> th ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | wl-luk-imtrdi.1 | |- ( ph -> ( ps -> ch ) ) |
|
| 2 | wl-luk-imtrdi.2 | |- ( ch -> th ) |
|
| 3 | 2 | wl-luk-imim2i | |- ( ( ps -> ch ) -> ( ps -> th ) ) |
| 4 | 1 3 | wl-luk-syl | |- ( ph -> ( ps -> th ) ) |