Step |
Hyp |
Ref |
Expression |
1 |
|
tfis2d.1 |
|- ( ph -> ( x = y -> ( ps <-> ch ) ) ) |
2 |
|
tfis2d.2 |
|- ( ph -> ( x e. On -> ( A. y e. x ch -> ps ) ) ) |
3 |
1
|
com12 |
|- ( x = y -> ( ph -> ( ps <-> ch ) ) ) |
4 |
3
|
pm5.74d |
|- ( x = y -> ( ( ph -> ps ) <-> ( ph -> ch ) ) ) |
5 |
|
r19.21v |
|- ( A. y e. x ( ph -> ch ) <-> ( ph -> A. y e. x ch ) ) |
6 |
2
|
com12 |
|- ( x e. On -> ( ph -> ( A. y e. x ch -> ps ) ) ) |
7 |
6
|
a2d |
|- ( x e. On -> ( ( ph -> A. y e. x ch ) -> ( ph -> ps ) ) ) |
8 |
5 7
|
syl5bi |
|- ( x e. On -> ( A. y e. x ( ph -> ch ) -> ( ph -> ps ) ) ) |
9 |
4 8
|
tfis2 |
|- ( x e. On -> ( ph -> ps ) ) |
10 |
9
|
com12 |
|- ( ph -> ( x e. On -> ps ) ) |