Description: Inference to extract one side of an implication from a definition. (Contributed by Jeff Hoffman, 18-Nov-2007) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | nic-bi1.1 | |- ( ( ph -/\ ps ) -/\ ( ( ph -/\ ph ) -/\ ( ps -/\ ps ) ) ) |
|
| Assertion | nic-bi1 | |- ( ph -/\ ( ps -/\ ps ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nic-bi1.1 | |- ( ( ph -/\ ps ) -/\ ( ( ph -/\ ph ) -/\ ( ps -/\ ps ) ) ) |
|
| 2 | nic-id | |- ( ph -/\ ( ph -/\ ph ) ) |
|
| 3 | 1 2 | nic-iimp1 | |- ( ph -/\ ( ph -/\ ps ) ) |
| 4 | 3 | nic-isw2 | |- ( ph -/\ ( ps -/\ ph ) ) |
| 5 | 4 | nic-idel | |- ( ph -/\ ( ps -/\ ps ) ) |