\iff真值表：(\false \iff A) \iff \neg
theorem false_iff_wff_iff_negself (A: wff): $ (\false \iff A) \iff \neg A $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | iff_tran | ((\false \iff A) \iff A \iff \false) \imp ((A \iff \false) \iff \neg A) \imp ((\false \iff A) \iff \neg A) |
|
| 2 | iff_comm | (\false \iff A) \iff A \iff \false |
|
| 3 | 1, 2 | ax_mp | ((A \iff \false) \iff \neg A) \imp ((\false \iff A) \iff \neg A) |
| 4 | wff_iff_false_iff_negself | (A \iff \false) \iff \neg A |
|
| 5 | 3, 4 | ax_mp | (\false \iff A) \iff \neg A |