Description: Introduction of a triple conjunct inside a contradiction. (Contributed by FL, 27-Dec-2007) (Proof shortened by Andrew Salmon, 26-Jun-2011)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | intn3and.1 | |- ( ph -> -. ps ) |
|
| Assertion | intn3an1d | |- ( ph -> -. ( ps /\ ch /\ th ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | intn3and.1 | |- ( ph -> -. ps ) |
|
| 2 | simp1 | |- ( ( ps /\ ch /\ th ) -> ps ) |
|
| 3 | 1 2 | nsyl | |- ( ph -> -. ( ps /\ ch /\ th ) ) |