Description: This theorem is in fact a copy of wl-luk-imtrdi , and repeated here to demonstrate a recursive proof scheme. The number '2' in the theorem name indicates that a chain of length 2 is modified. (Contributed by Wolf Lammen, 6-Jul-2019) (New usage is discouraged.) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | wl-impchain-mp-2.a | |- ( th -> ( ch -> ps ) ) |
|
| wl-impchain-mp-2.b | |- ( ps -> ph ) |
||
| Assertion | wl-impchain-mp-2 | |- ( th -> ( ch -> ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | wl-impchain-mp-2.a | |- ( th -> ( ch -> ps ) ) |
|
| 2 | wl-impchain-mp-2.b | |- ( ps -> ph ) |
|
| 3 | 2 | wl-luk-imim2i | |- ( ( ch -> ps ) -> ( ch -> ph ) ) |
| 4 | 1 3 | wl-impchain-mp-1 | |- ( th -> ( ch -> ph ) ) |