Step |
Hyp |
Ref |
Expression |
1 |
|
biimp |
|- ( ( ph <-> ps ) -> ( ph -> ps ) ) |
2 |
1
|
alimi |
|- ( A. x ( ph <-> ps ) -> A. x ( ph -> ps ) ) |
3 |
|
spsbim |
|- ( A. x ( ph -> ps ) -> ( [ t / x ] ph -> [ t / x ] ps ) ) |
4 |
2 3
|
syl |
|- ( A. x ( ph <-> ps ) -> ( [ t / x ] ph -> [ t / x ] ps ) ) |
5 |
|
biimpr |
|- ( ( ph <-> ps ) -> ( ps -> ph ) ) |
6 |
5
|
alimi |
|- ( A. x ( ph <-> ps ) -> A. x ( ps -> ph ) ) |
7 |
|
spsbim |
|- ( A. x ( ps -> ph ) -> ( [ t / x ] ps -> [ t / x ] ph ) ) |
8 |
6 7
|
syl |
|- ( A. x ( ph <-> ps ) -> ( [ t / x ] ps -> [ t / x ] ph ) ) |
9 |
4 8
|
impbid |
|- ( A. x ( ph <-> ps ) -> ( [ t / x ] ph <-> [ t / x ] ps ) ) |