Description: Deduction for elimination by cases. (Contributed by NM, 24-May-2013)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ecase3ad.1 | |- ( ph -> ( ps -> th ) ) |
|
ecase3ad.2 | |- ( ph -> ( ch -> th ) ) |
||
ecase3ad.3 | |- ( ph -> ( ( -. ps /\ -. ch ) -> th ) ) |
||
Assertion | ecase3ad | |- ( ph -> th ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ecase3ad.1 | |- ( ph -> ( ps -> th ) ) |
|
2 | ecase3ad.2 | |- ( ph -> ( ch -> th ) ) |
|
3 | ecase3ad.3 | |- ( ph -> ( ( -. ps /\ -. ch ) -> th ) ) |
|
4 | notnotr | |- ( -. -. ps -> ps ) |
|
5 | 4 1 | syl5 | |- ( ph -> ( -. -. ps -> th ) ) |
6 | notnotr | |- ( -. -. ch -> ch ) |
|
7 | 6 2 | syl5 | |- ( ph -> ( -. -. ch -> th ) ) |
8 | 5 7 3 | ecased | |- ( ph -> th ) |