Step |
Hyp |
Ref |
Expression |
1 |
|
an2anr |
|- ( ( ( ps /\ ch ) /\ ( th /\ ph ) ) <-> ( ( ch /\ ps ) /\ ( ph /\ th ) ) ) |
2 |
|
an2anr |
|- ( ( ( ph /\ ch ) /\ ( th /\ ps ) ) <-> ( ( ch /\ ph ) /\ ( ps /\ th ) ) ) |
3 |
|
an4 |
|- ( ( ( ch /\ ph ) /\ ( ps /\ th ) ) <-> ( ( ch /\ ps ) /\ ( ph /\ th ) ) ) |
4 |
2 3
|
bitri |
|- ( ( ( ph /\ ch ) /\ ( th /\ ps ) ) <-> ( ( ch /\ ps ) /\ ( ph /\ th ) ) ) |
5 |
|
an43 |
|- ( ( ( ph /\ ch ) /\ ( th /\ ps ) ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) ) ) |
6 |
1 4 5
|
3bitr2ri |
|- ( ( ( ph /\ ps ) /\ ( ch /\ th ) ) <-> ( ( ps /\ ch ) /\ ( th /\ ph ) ) ) |
7 |
|
3an4anass |
|- ( ( ( ps /\ ch /\ th ) /\ ph ) <-> ( ( ps /\ ch ) /\ ( th /\ ph ) ) ) |
8 |
|
ancom |
|- ( ( ( ps /\ ch /\ th ) /\ ph ) <-> ( ph /\ ( ps /\ ch /\ th ) ) ) |
9 |
6 7 8
|
3bitr2ri |
|- ( ( ph /\ ( ps /\ ch /\ th ) ) <-> ( ( ph /\ ps ) /\ ( ch /\ th ) ) ) |