Step |
Hyp |
Ref |
Expression |
1 |
|
uun2221p2.1 |
|- ( ( ( ps /\ ph ) /\ ph /\ ph ) -> ch ) |
2 |
|
3anrev |
|- ( ( ph /\ ph /\ ( ps /\ ph ) ) <-> ( ( ps /\ ph ) /\ ph /\ ph ) ) |
3 |
2
|
imbi1i |
|- ( ( ( ph /\ ph /\ ( ps /\ ph ) ) -> ch ) <-> ( ( ( ps /\ ph ) /\ ph /\ ph ) -> ch ) ) |
4 |
1 3
|
mpbir |
|- ( ( ph /\ ph /\ ( ps /\ ph ) ) -> ch ) |
5 |
|
3anass |
|- ( ( ph /\ ph /\ ( ps /\ ph ) ) <-> ( ph /\ ( ph /\ ( ps /\ ph ) ) ) ) |
6 |
|
anabs5 |
|- ( ( ph /\ ( ph /\ ( ps /\ ph ) ) ) <-> ( ph /\ ( ps /\ ph ) ) ) |
7 |
5 6
|
bitri |
|- ( ( ph /\ ph /\ ( ps /\ ph ) ) <-> ( ph /\ ( ps /\ ph ) ) ) |
8 |
|
ancom |
|- ( ( ph /\ ps ) <-> ( ps /\ ph ) ) |
9 |
8
|
anbi2i |
|- ( ( ph /\ ( ph /\ ps ) ) <-> ( ph /\ ( ps /\ ph ) ) ) |
10 |
7 9
|
bitr4i |
|- ( ( ph /\ ph /\ ( ps /\ ph ) ) <-> ( ph /\ ( ph /\ ps ) ) ) |
11 |
|
anabs5 |
|- ( ( ph /\ ( ph /\ ps ) ) <-> ( ph /\ ps ) ) |
12 |
11 8
|
bitri |
|- ( ( ph /\ ( ph /\ ps ) ) <-> ( ps /\ ph ) ) |
13 |
10 12
|
bitri |
|- ( ( ph /\ ph /\ ( ps /\ ph ) ) <-> ( ps /\ ph ) ) |
14 |
13
|
imbi1i |
|- ( ( ( ph /\ ph /\ ( ps /\ ph ) ) -> ch ) <-> ( ( ps /\ ph ) -> ch ) ) |
15 |
4 14
|
mpbi |
|- ( ( ps /\ ph ) -> ch ) |