Description: Derive the standard modus ponens from nic-mp . (Contributed by Jeff Hoffman, 18-Nov-2007) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | nic-smin | |- ph |
|
| nic-smaj | |- ( ph -> ps ) |
||
| Assertion | nic-stdmp | |- ps |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nic-smin | |- ph |
|
| 2 | nic-smaj | |- ( ph -> ps ) |
|
| 3 | nic-dfim | |- ( ( ( ph -/\ ( ps -/\ ps ) ) -/\ ( ph -> ps ) ) -/\ ( ( ( ph -/\ ( ps -/\ ps ) ) -/\ ( ph -/\ ( ps -/\ ps ) ) ) -/\ ( ( ph -> ps ) -/\ ( ph -> ps ) ) ) ) |
|
| 4 | 3 | nic-bi2 | |- ( ( ph -> ps ) -/\ ( ( ph -/\ ( ps -/\ ps ) ) -/\ ( ph -/\ ( ps -/\ ps ) ) ) ) |
| 5 | 2 4 | nic-mp | |- ( ph -/\ ( ps -/\ ps ) ) |
| 6 | 1 5 | nic-mp | |- ps |