Step |
Hyp |
Ref |
Expression |
1 |
|
cbvmovw.1 |
|- ( x = y -> ( ph <-> ps ) ) |
2 |
|
df-mo |
|- ( E* x ph <-> E. z A. x ( ph -> x = z ) ) |
3 |
|
equequ1 |
|- ( x = y -> ( x = z <-> y = z ) ) |
4 |
1 3
|
imbi12d |
|- ( x = y -> ( ( ph -> x = z ) <-> ( ps -> y = z ) ) ) |
5 |
4
|
cbvalvw |
|- ( A. x ( ph -> x = z ) <-> A. y ( ps -> y = z ) ) |
6 |
5
|
exbii |
|- ( E. z A. x ( ph -> x = z ) <-> E. z A. y ( ps -> y = z ) ) |
7 |
|
df-mo |
|- ( E* y ps <-> E. z A. y ( ps -> y = z ) ) |
8 |
7
|
bicomi |
|- ( E. z A. y ( ps -> y = z ) <-> E* y ps ) |
9 |
2 6 8
|
3bitri |
|- ( E* x ph <-> E* y ps ) |