Description: Inference for swapping nested terms. (Contributed by Jeff Hoffman, 17-Nov-2007) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | nic-isw2.1 | |- ( ps -/\ ( th -/\ ph ) ) |
|
| Assertion | nic-isw2 | |- ( ps -/\ ( ph -/\ th ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nic-isw2.1 | |- ( ps -/\ ( th -/\ ph ) ) |
|
| 2 | nic-swap | |- ( ( ph -/\ th ) -/\ ( ( th -/\ ph ) -/\ ( th -/\ ph ) ) ) |
|
| 3 | 2 | nic-imp | |- ( ( ps -/\ ( th -/\ ph ) ) -/\ ( ( ( ph -/\ th ) -/\ ps ) -/\ ( ( ph -/\ th ) -/\ ps ) ) ) |
| 4 | 1 3 | nic-mp | |- ( ( ph -/\ th ) -/\ ps ) |
| 5 | 4 | nic-isw1 | |- ( ps -/\ ( ph -/\ th ) ) |