Description: Importation inference. (Contributed by NM, 3-Jan-1993) (Proof shortened by Eric Schmidt, 22-Dec-2006)
Ref | Expression | ||
---|---|---|---|
Hypothesis | imp.1 | |- ( ph -> ( ps -> ch ) ) |
|
Assertion | imp | |- ( ( ph /\ ps ) -> ch ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imp.1 | |- ( ph -> ( ps -> ch ) ) |
|
2 | df-an | |- ( ( ph /\ ps ) <-> -. ( ph -> -. ps ) ) |
|
3 | 1 | impi | |- ( -. ( ph -> -. ps ) -> ch ) |
4 | 2 3 | sylbi | |- ( ( ph /\ ps ) -> ch ) |