Step |
Hyp |
Ref |
Expression |
1 |
|
cadan |
|- ( cadd ( ph , ps , ch ) <-> ( ( ph \/ ps ) /\ ( ph \/ ch ) /\ ( ps \/ ch ) ) ) |
2 |
|
3anass |
|- ( ( ( ph \/ ps ) /\ ( ph \/ ch ) /\ ( ps \/ ch ) ) <-> ( ( ph \/ ps ) /\ ( ( ph \/ ch ) /\ ( ps \/ ch ) ) ) ) |
3 |
1 2
|
bitri |
|- ( cadd ( ph , ps , ch ) <-> ( ( ph \/ ps ) /\ ( ( ph \/ ch ) /\ ( ps \/ ch ) ) ) ) |
4 |
|
olc |
|- ( ch -> ( ph \/ ch ) ) |
5 |
|
olc |
|- ( ch -> ( ps \/ ch ) ) |
6 |
4 5
|
jca |
|- ( ch -> ( ( ph \/ ch ) /\ ( ps \/ ch ) ) ) |
7 |
6
|
biantrud |
|- ( ch -> ( ( ph \/ ps ) <-> ( ( ph \/ ps ) /\ ( ( ph \/ ch ) /\ ( ps \/ ch ) ) ) ) ) |
8 |
3 7
|
bitr4id |
|- ( ch -> ( cadd ( ph , ps , ch ) <-> ( ph \/ ps ) ) ) |