Description: A formula is equivalent to its negation implying it. Theorem *4.81 of WhiteheadRussell p. 122. Note that the second step, using pm2.24 , could also use ax-1 . (Contributed by NM, 3-Jan-2005)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | pm4.81 | |- ( ( -. ph -> ph ) <-> ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm2.18 | |- ( ( -. ph -> ph ) -> ph ) |
|
| 2 | pm2.24 | |- ( ph -> ( -. ph -> ph ) ) |
|
| 3 | 1 2 | impbii | |- ( ( -. ph -> ph ) <-> ph ) |