Description: Inference to extract the other side of an implication from a 'biconditional' definition. (Contributed by Jeff Hoffman, 18-Nov-2007) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | nic-bi2.1 | |- ( ( ph -/\ ps ) -/\ ( ( ph -/\ ph ) -/\ ( ps -/\ ps ) ) ) |
|
| Assertion | nic-bi2 | |- ( ps -/\ ( ph -/\ ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nic-bi2.1 | |- ( ( ph -/\ ps ) -/\ ( ( ph -/\ ph ) -/\ ( ps -/\ ps ) ) ) |
|
| 2 | 1 | nic-isw2 | |- ( ( ph -/\ ps ) -/\ ( ( ps -/\ ps ) -/\ ( ph -/\ ph ) ) ) |
| 3 | nic-id | |- ( ps -/\ ( ps -/\ ps ) ) |
|
| 4 | 2 3 | nic-iimp1 | |- ( ps -/\ ( ph -/\ ps ) ) |
| 5 | 4 | nic-idel | |- ( ps -/\ ( ph -/\ ph ) ) |