Step |
Hyp |
Ref |
Expression |
1 |
|
bj-nnclav |
|- ( ( ( ( ( ( ph -> ps ) -> ch ) -> ph ) -> ch ) -> ( ( ( ph -> ps ) -> ch ) -> ph ) ) -> ( ( ( ( ( ph -> ps ) -> ch ) -> ph ) -> ch ) -> ch ) ) |
2 |
|
ax-1 |
|- ( ch -> ( ( ph -> ps ) -> ch ) ) |
3 |
2
|
imim2i |
|- ( ( ( ( ( ph -> ps ) -> ch ) -> ph ) -> ch ) -> ( ( ( ( ph -> ps ) -> ch ) -> ph ) -> ( ( ph -> ps ) -> ch ) ) ) |
4 |
|
peirce |
|- ( ( ( ( ( ph -> ps ) -> ch ) -> ph ) -> ( ( ph -> ps ) -> ch ) ) -> ( ( ph -> ps ) -> ch ) ) |
5 |
3 4
|
syl |
|- ( ( ( ( ( ph -> ps ) -> ch ) -> ph ) -> ch ) -> ( ( ph -> ps ) -> ch ) ) |
6 |
|
imim2 |
|- ( ( ch -> ph ) -> ( ( ( ph -> ps ) -> ch ) -> ( ( ph -> ps ) -> ph ) ) ) |
7 |
|
peirce |
|- ( ( ( ph -> ps ) -> ph ) -> ph ) |
8 |
5 6 7
|
syl56 |
|- ( ( ch -> ph ) -> ( ( ( ( ( ph -> ps ) -> ch ) -> ph ) -> ch ) -> ph ) ) |
9 |
8
|
a1dd |
|- ( ( ch -> ph ) -> ( ( ( ( ( ph -> ps ) -> ch ) -> ph ) -> ch ) -> ( ( ( ph -> ps ) -> ch ) -> ph ) ) ) |
10 |
1 9
|
syl11 |
|- ( ( ( ( ( ph -> ps ) -> ch ) -> ph ) -> ch ) -> ( ( ch -> ph ) -> ch ) ) |
11 |
|
peirce |
|- ( ( ( ch -> ph ) -> ch ) -> ch ) |
12 |
10 11
|
syl |
|- ( ( ( ( ( ph -> ps ) -> ch ) -> ph ) -> ch ) -> ch ) |