\or真值表：\false \or wff \iff wff
theorem false_or_wff_iff_wff (A: wff): $ \false \or A \iff A $;
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | iff_tran | (\false \or A \iff A \or \false) \imp (A \or \false \iff A) \imp (\false \or A \iff A) |
|
| 2 | or_comm | \false \or A \iff A \or \false |
|
| 3 | 1, 2 | ax_mp | (A \or \false \iff A) \imp (\false \or A \iff A) |
| 4 | wff_or_false_iff_wff | A \or \false \iff A |
|
| 5 | 3, 4 | ax_mp | \false \or A \iff A |