Step |
Hyp |
Ref |
Expression |
1 |
|
eel2122old.1 |
|- ( ( ph /\ ps ) -> ch ) |
2 |
|
eel2122old.2 |
|- ( ps -> th ) |
3 |
|
eel2122old.3 |
|- ( ps -> ta ) |
4 |
|
eel2122old.4 |
|- ( ( ch /\ th /\ ta ) -> et ) |
5 |
4
|
3exp |
|- ( ch -> ( th -> ( ta -> et ) ) ) |
6 |
1 5
|
syl |
|- ( ( ph /\ ps ) -> ( th -> ( ta -> et ) ) ) |
7 |
2 6
|
syl5 |
|- ( ( ph /\ ps ) -> ( ps -> ( ta -> et ) ) ) |
8 |
3 7
|
syl7 |
|- ( ( ph /\ ps ) -> ( ps -> ( ps -> et ) ) ) |
9 |
8
|
ex |
|- ( ph -> ( ps -> ( ps -> ( ps -> et ) ) ) ) |
10 |
9
|
pm2.43d |
|- ( ph -> ( ps -> ( ps -> et ) ) ) |
11 |
10
|
pm2.43d |
|- ( ph -> ( ps -> et ) ) |
12 |
11
|
imp |
|- ( ( ph /\ ps ) -> et ) |