Step |
Hyp |
Ref |
Expression |
1 |
|
merco2 |
|- ( ( ( ph -> ph ) -> ( ( F. -> ph ) -> ph ) ) -> ( ( ph -> ph ) -> ( ph -> ( ph -> ph ) ) ) ) |
2 |
|
mercolem3 |
|- ( ( ( ph -> ch ) -> ( th -> ps ) ) -> ( ( ph -> ch ) -> ( ( ( ph -> ch ) -> ( th -> ps ) ) -> ( th -> ps ) ) ) ) |
3 |
|
mercolem6 |
|- ( ( ( ( ph -> ch ) -> ( th -> ps ) ) -> ( ( ph -> ch ) -> ( ( ( ph -> ch ) -> ( th -> ps ) ) -> ( th -> ps ) ) ) ) -> ( ( ph -> ch ) -> ( ( ( ph -> ch ) -> ( th -> ps ) ) -> ( th -> ps ) ) ) ) |
4 |
2 3
|
ax-mp |
|- ( ( ph -> ch ) -> ( ( ( ph -> ch ) -> ( th -> ps ) ) -> ( th -> ps ) ) ) |
5 |
|
mercolem5 |
|- ( ph -> ( ( ph -> ps ) -> ( ( ( ph -> ch ) -> ( th -> ps ) ) -> ( th -> ps ) ) ) ) |
6 |
|
mercolem4 |
|- ( ( ph -> ( ( ph -> ps ) -> ( ( ( ph -> ch ) -> ( th -> ps ) ) -> ( th -> ps ) ) ) ) -> ( ( ( ph -> ch ) -> ( ( ( ph -> ch ) -> ( th -> ps ) ) -> ( th -> ps ) ) ) -> ( ( ( ( ph -> ph ) -> ( ( F. -> ph ) -> ph ) ) -> ( ( ph -> ph ) -> ( ph -> ( ph -> ph ) ) ) ) -> ( ( ph -> ps ) -> ( ( ( ph -> ch ) -> ( th -> ps ) ) -> ( th -> ps ) ) ) ) ) ) |
7 |
5 6
|
ax-mp |
|- ( ( ( ph -> ch ) -> ( ( ( ph -> ch ) -> ( th -> ps ) ) -> ( th -> ps ) ) ) -> ( ( ( ( ph -> ph ) -> ( ( F. -> ph ) -> ph ) ) -> ( ( ph -> ph ) -> ( ph -> ( ph -> ph ) ) ) ) -> ( ( ph -> ps ) -> ( ( ( ph -> ch ) -> ( th -> ps ) ) -> ( th -> ps ) ) ) ) ) |
8 |
4 7
|
ax-mp |
|- ( ( ( ( ph -> ph ) -> ( ( F. -> ph ) -> ph ) ) -> ( ( ph -> ph ) -> ( ph -> ( ph -> ph ) ) ) ) -> ( ( ph -> ps ) -> ( ( ( ph -> ch ) -> ( th -> ps ) ) -> ( th -> ps ) ) ) ) |
9 |
1 8
|
ax-mp |
|- ( ( ph -> ps ) -> ( ( ( ph -> ch ) -> ( th -> ps ) ) -> ( th -> ps ) ) ) |