Description: Move negation outside of biconditional. Compare Theorem *5.18 of WhiteheadRussell p. 124. (Contributed by NM, 27-Jun-2002) (Proof shortened by Wolf Lammen, 20-Sep-2013) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | nbbn | |- ( ( -. ph <-> ps ) <-> -. ( ph <-> ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | pm5.18 | |- ( ( -. ph <-> ps ) <-> -. ( -. ph <-> -. ps ) ) |
|
| 2 | notbi | |- ( ( ph <-> ps ) <-> ( -. ph <-> -. ps ) ) |
|
| 3 | 1 2 | xchbinxr | |- ( ( -. ph <-> ps ) <-> -. ( ph <-> ps ) ) |