Description: Implication in terms of conjunction and negation. Theorem 3.4(27) of Stoll p. 176. (Contributed by NM, 12-Mar-1993) (Proof shortened by Wolf Lammen, 30-Oct-2012)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | iman | |- ( ( ph -> ps ) <-> -. ( ph /\ -. ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | notnotb | |- ( ps <-> -. -. ps ) |
|
| 2 | 1 | imbi2i | |- ( ( ph -> ps ) <-> ( ph -> -. -. ps ) ) |
| 3 | imnan | |- ( ( ph -> -. -. ps ) <-> -. ( ph /\ -. ps ) ) |
|
| 4 | 2 3 | bitri | |- ( ( ph -> ps ) <-> -. ( ph /\ -. ps ) ) |