\iff真值表：(\false \iff \true) \iff \false
theorem false_iff_true_iff_false: $ (\false \iff \true) \iff \false $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | iff_tran | ((\false \iff \true) \iff \true \iff \false) \imp ((\true \iff \false) \iff \false) \imp ((\false \iff \true) \iff \false) |
|
| 2 | iff_comm | (\false \iff \true) \iff \true \iff \false |
|
| 3 | 1, 2 | ax_mp | ((\true \iff \false) \iff \false) \imp ((\false \iff \true) \iff \false) |
| 4 | true_iff_false_iff_false | (\true \iff \false) \iff \false |
|
| 5 | 3, 4 | ax_mp | (\false \iff \true) \iff \false |