Step |
Hyp |
Ref |
Expression |
1 |
|
19.35 |
|- ( E. x ( ph -> ps ) <-> ( A. x ph -> E. x ps ) ) |
2 |
|
id |
|- ( F/ x ph -> F/ x ph ) |
3 |
2
|
nfrd |
|- ( F/ x ph -> ( E. x ph -> A. x ph ) ) |
4 |
3
|
imim1d |
|- ( F/ x ph -> ( ( A. x ph -> E. x ps ) -> ( E. x ph -> E. x ps ) ) ) |
5 |
1 4
|
syl5bi |
|- ( F/ x ph -> ( E. x ( ph -> ps ) -> ( E. x ph -> E. x ps ) ) ) |
6 |
|
id |
|- ( F/ x ps -> F/ x ps ) |
7 |
6
|
nfrd |
|- ( F/ x ps -> ( E. x ps -> A. x ps ) ) |
8 |
7
|
imim2d |
|- ( F/ x ps -> ( ( E. x ph -> E. x ps ) -> ( E. x ph -> A. x ps ) ) ) |
9 |
|
19.38 |
|- ( ( E. x ph -> A. x ps ) -> A. x ( ph -> ps ) ) |
10 |
8 9
|
syl6 |
|- ( F/ x ps -> ( ( E. x ph -> E. x ps ) -> A. x ( ph -> ps ) ) ) |
11 |
5 10
|
syl9 |
|- ( F/ x ph -> ( F/ x ps -> ( E. x ( ph -> ps ) -> A. x ( ph -> ps ) ) ) ) |
12 |
|
df-nf |
|- ( F/ x ( ph -> ps ) <-> ( E. x ( ph -> ps ) -> A. x ( ph -> ps ) ) ) |
13 |
11 12
|
syl6ibr |
|- ( F/ x ph -> ( F/ x ps -> F/ x ( ph -> ps ) ) ) |