Description: Double the terms. Since doubling is the same as negation, this can be viewed as a contraposition inference. (Contributed by Jeff Hoffman, 17-Nov-2007) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | nic-idbl.1 | |- ( ph -/\ ( ps -/\ ps ) ) |
|
| Assertion | nic-idbl | |- ( ( ps -/\ ps ) -/\ ( ( ph -/\ ph ) -/\ ( ph -/\ ph ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nic-idbl.1 | |- ( ph -/\ ( ps -/\ ps ) ) |
|
| 2 | 1 | nic-imp | |- ( ( ps -/\ ps ) -/\ ( ( ph -/\ ps ) -/\ ( ph -/\ ps ) ) ) |
| 3 | 1 | nic-imp | |- ( ( ph -/\ ps ) -/\ ( ( ph -/\ ph ) -/\ ( ph -/\ ph ) ) ) |
| 4 | 2 3 | nic-ich | |- ( ( ps -/\ ps ) -/\ ( ( ph -/\ ph ) -/\ ( ph -/\ ph ) ) ) |