Description: A lemma for Conjunctive Normal Form unit propagation, in deduction form. (Contributed by Giovanni Mascellani, 15-Sep-2017) (Proof shortened by Wolf Lammen, 13-Apr-2024)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | olcnd.1 | |- ( ph -> ( ps \/ ch ) ) |
|
| olcnd.2 | |- ( ph -> -. ch ) |
||
| Assertion | olcnd | |- ( ph -> ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | olcnd.1 | |- ( ph -> ( ps \/ ch ) ) |
|
| 2 | olcnd.2 | |- ( ph -> -. ch ) |
|
| 3 | 1 | ord | |- ( ph -> ( -. ps -> ch ) ) |
| 4 | 2 3 | mt3d | |- ( ph -> ps ) |