Step |
Hyp |
Ref |
Expression |
1 |
|
merco1lem5 |
|- ( ( ( ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> F. ) -> F. ) -> F. ) -> ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> F. ) ) |
2 |
|
merco1lem3 |
|- ( ( ( ( ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> F. ) -> F. ) -> F. ) -> ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> F. ) ) -> ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> ( ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> F. ) -> F. ) ) ) |
3 |
1 2
|
ax-mp |
|- ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> ( ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> F. ) -> F. ) ) |
4 |
|
merco1lem5 |
|- ( ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> ( ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> F. ) -> F. ) ) -> ( ( ph -> ps ) -> ( ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> F. ) -> F. ) ) ) |
5 |
3 4
|
ax-mp |
|- ( ( ph -> ps ) -> ( ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> F. ) -> F. ) ) |
6 |
|
merco1lem3 |
|- ( ( ( ph -> ps ) -> ( ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> F. ) -> F. ) ) -> ( ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> F. ) -> ph ) ) |
7 |
5 6
|
ax-mp |
|- ( ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> F. ) -> ph ) |
8 |
|
merco1 |
|- ( ( ( ( ( ( ph -> ps ) -> F. ) -> ( ch -> F. ) ) -> F. ) -> ph ) -> ( ( ph -> ( ph -> ps ) ) -> ( ch -> ( ph -> ps ) ) ) ) |
9 |
7 8
|
ax-mp |
|- ( ( ph -> ( ph -> ps ) ) -> ( ch -> ( ph -> ps ) ) ) |