Step |
Hyp |
Ref |
Expression |
1 |
|
merco1 |
|- ( ( ( ( ( F. -> ph ) -> ( ph -> F. ) ) -> ( ph -> F. ) ) -> ( F. -> ph ) ) -> ( ( ( F. -> ph ) -> F. ) -> ( ph -> F. ) ) ) |
2 |
|
merco1 |
|- ( ( ( ( ( ( F. -> ph ) -> ( ph -> F. ) ) -> ( ph -> F. ) ) -> ( F. -> ph ) ) -> ( ( ( F. -> ph ) -> F. ) -> ( ph -> F. ) ) ) -> ( ( ( ( ( F. -> ph ) -> F. ) -> ( ph -> F. ) ) -> ( F. -> ph ) ) -> ( ph -> ( F. -> ph ) ) ) ) |
3 |
1 2
|
ax-mp |
|- ( ( ( ( ( F. -> ph ) -> F. ) -> ( ph -> F. ) ) -> ( F. -> ph ) ) -> ( ph -> ( F. -> ph ) ) ) |
4 |
|
merco1 |
|- ( ( ( ( ( ( F. -> ph ) -> F. ) -> ( ph -> F. ) ) -> ( F. -> ph ) ) -> ( ph -> ( F. -> ph ) ) ) -> ( ( ( ph -> ( F. -> ph ) ) -> ( F. -> ph ) ) -> ( ph -> ( F. -> ph ) ) ) ) |
5 |
3 4
|
ax-mp |
|- ( ( ( ph -> ( F. -> ph ) ) -> ( F. -> ph ) ) -> ( ph -> ( F. -> ph ) ) ) |
6 |
|
merco1 |
|- ( ( ( ( ( F. -> ph ) -> ( ph -> F. ) ) -> ( ( ph -> ( F. -> ph ) ) -> F. ) ) -> ( ph -> ( F. -> ph ) ) ) -> ( ( ( ph -> ( F. -> ph ) ) -> F. ) -> ( ph -> F. ) ) ) |
7 |
|
merco1 |
|- ( ( ( ( ( ( F. -> ph ) -> ( ph -> F. ) ) -> ( ( ph -> ( F. -> ph ) ) -> F. ) ) -> ( ph -> ( F. -> ph ) ) ) -> ( ( ( ph -> ( F. -> ph ) ) -> F. ) -> ( ph -> F. ) ) ) -> ( ( ( ( ( ph -> ( F. -> ph ) ) -> F. ) -> ( ph -> F. ) ) -> ( F. -> ph ) ) -> ( ( ph -> ( F. -> ph ) ) -> ( F. -> ph ) ) ) ) |
8 |
6 7
|
ax-mp |
|- ( ( ( ( ( ph -> ( F. -> ph ) ) -> F. ) -> ( ph -> F. ) ) -> ( F. -> ph ) ) -> ( ( ph -> ( F. -> ph ) ) -> ( F. -> ph ) ) ) |
9 |
|
merco1 |
|- ( ( ( ( ( ( ph -> ( F. -> ph ) ) -> F. ) -> ( ph -> F. ) ) -> ( F. -> ph ) ) -> ( ( ph -> ( F. -> ph ) ) -> ( F. -> ph ) ) ) -> ( ( ( ( ph -> ( F. -> ph ) ) -> ( F. -> ph ) ) -> ( ph -> ( F. -> ph ) ) ) -> ( ph -> ( ph -> ( F. -> ph ) ) ) ) ) |
10 |
8 9
|
ax-mp |
|- ( ( ( ( ph -> ( F. -> ph ) ) -> ( F. -> ph ) ) -> ( ph -> ( F. -> ph ) ) ) -> ( ph -> ( ph -> ( F. -> ph ) ) ) ) |
11 |
5 10
|
ax-mp |
|- ( ph -> ( ph -> ( F. -> ph ) ) ) |
12 |
|
merco1 |
|- ( ( ( ( ( F. -> ph ) -> ( ph -> F. ) ) -> ( ph -> F. ) ) -> ( F. -> ch ) ) -> ( ( ( F. -> ch ) -> F. ) -> ( ph -> F. ) ) ) |
13 |
|
merco1 |
|- ( ( ( ( ( ( F. -> ph ) -> ( ph -> F. ) ) -> ( ph -> F. ) ) -> ( F. -> ch ) ) -> ( ( ( F. -> ch ) -> F. ) -> ( ph -> F. ) ) ) -> ( ( ( ( ( F. -> ch ) -> F. ) -> ( ph -> F. ) ) -> ( F. -> ph ) ) -> ( ph -> ( F. -> ph ) ) ) ) |
14 |
12 13
|
ax-mp |
|- ( ( ( ( ( F. -> ch ) -> F. ) -> ( ph -> F. ) ) -> ( F. -> ph ) ) -> ( ph -> ( F. -> ph ) ) ) |
15 |
|
merco1 |
|- ( ( ( ( ( ( F. -> ch ) -> F. ) -> ( ph -> F. ) ) -> ( F. -> ph ) ) -> ( ph -> ( F. -> ph ) ) ) -> ( ( ( ph -> ( F. -> ph ) ) -> ( F. -> ch ) ) -> ( ph -> ( F. -> ch ) ) ) ) |
16 |
14 15
|
ax-mp |
|- ( ( ( ph -> ( F. -> ph ) ) -> ( F. -> ch ) ) -> ( ph -> ( F. -> ch ) ) ) |
17 |
|
merco1 |
|- ( ( ( ( ( F. -> ch ) -> ( ( ph -> ( ph -> ( F. -> ph ) ) ) -> F. ) ) -> ( ( ph -> ( F. -> ph ) ) -> F. ) ) -> ( ph -> ( F. -> ch ) ) ) -> ( ( ( ph -> ( F. -> ch ) ) -> F. ) -> ( ( ph -> ( ph -> ( F. -> ph ) ) ) -> F. ) ) ) |
18 |
|
merco1 |
|- ( ( ( ( ( ( F. -> ch ) -> ( ( ph -> ( ph -> ( F. -> ph ) ) ) -> F. ) ) -> ( ( ph -> ( F. -> ph ) ) -> F. ) ) -> ( ph -> ( F. -> ch ) ) ) -> ( ( ( ph -> ( F. -> ch ) ) -> F. ) -> ( ( ph -> ( ph -> ( F. -> ph ) ) ) -> F. ) ) ) -> ( ( ( ( ( ph -> ( F. -> ch ) ) -> F. ) -> ( ( ph -> ( ph -> ( F. -> ph ) ) ) -> F. ) ) -> ( F. -> ch ) ) -> ( ( ph -> ( F. -> ph ) ) -> ( F. -> ch ) ) ) ) |
19 |
17 18
|
ax-mp |
|- ( ( ( ( ( ph -> ( F. -> ch ) ) -> F. ) -> ( ( ph -> ( ph -> ( F. -> ph ) ) ) -> F. ) ) -> ( F. -> ch ) ) -> ( ( ph -> ( F. -> ph ) ) -> ( F. -> ch ) ) ) |
20 |
|
merco1 |
|- ( ( ( ( ( ( ph -> ( F. -> ch ) ) -> F. ) -> ( ( ph -> ( ph -> ( F. -> ph ) ) ) -> F. ) ) -> ( F. -> ch ) ) -> ( ( ph -> ( F. -> ph ) ) -> ( F. -> ch ) ) ) -> ( ( ( ( ph -> ( F. -> ph ) ) -> ( F. -> ch ) ) -> ( ph -> ( F. -> ch ) ) ) -> ( ( ph -> ( ph -> ( F. -> ph ) ) ) -> ( ph -> ( F. -> ch ) ) ) ) ) |
21 |
19 20
|
ax-mp |
|- ( ( ( ( ph -> ( F. -> ph ) ) -> ( F. -> ch ) ) -> ( ph -> ( F. -> ch ) ) ) -> ( ( ph -> ( ph -> ( F. -> ph ) ) ) -> ( ph -> ( F. -> ch ) ) ) ) |
22 |
16 21
|
ax-mp |
|- ( ( ph -> ( ph -> ( F. -> ph ) ) ) -> ( ph -> ( F. -> ch ) ) ) |
23 |
11 22
|
ax-mp |
|- ( ph -> ( F. -> ch ) ) |