Description: Deduction conjoining the consequents of two implications. Deduction form of jca and double deduction form of pm3.2 and pm3.2i . (Contributed by NM, 15-Jul-1993) (Proof shortened by Wolf Lammen, 23-Jul-2013)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | jcad.1 | |- ( ph -> ( ps -> ch ) ) |
|
| jcad.2 | |- ( ph -> ( ps -> th ) ) |
||
| Assertion | jcad | |- ( ph -> ( ps -> ( ch /\ th ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | jcad.1 | |- ( ph -> ( ps -> ch ) ) |
|
| 2 | jcad.2 | |- ( ph -> ( ps -> th ) ) |
|
| 3 | pm3.2 | |- ( ch -> ( th -> ( ch /\ th ) ) ) |
|
| 4 | 1 2 3 | syl6c | |- ( ph -> ( ps -> ( ch /\ th ) ) ) |