Description: This theorem "defines" negation in terms of 'nand'. Analogous to nannot . In a pure (standalone) treatment of Nicod's axiom, this theorem would be changed to a definition ($a statement). (Contributed by NM, 11-Dec-2008) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | nic-dfneg | |- ( ( ( ph -/\ ph ) -/\ -. ph ) -/\ ( ( ( ph -/\ ph ) -/\ ( ph -/\ ph ) ) -/\ ( -. ph -/\ -. ph ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nannot | |- ( -. ph <-> ( ph -/\ ph ) ) |
|
| 2 | 1 | bicomi | |- ( ( ph -/\ ph ) <-> -. ph ) |
| 3 | nanbi | |- ( ( ( ph -/\ ph ) <-> -. ph ) <-> ( ( ( ph -/\ ph ) -/\ -. ph ) -/\ ( ( ( ph -/\ ph ) -/\ ( ph -/\ ph ) ) -/\ ( -. ph -/\ -. ph ) ) ) ) |
|
| 4 | 2 3 | mpbi | |- ( ( ( ph -/\ ph ) -/\ -. ph ) -/\ ( ( ( ph -/\ ph ) -/\ ( ph -/\ ph ) ) -/\ ( -. ph -/\ -. ph ) ) ) |