Step |
Hyp |
Ref |
Expression |
1 |
|
andi |
|- ( ( ph /\ ( ps \/ ch ) ) <-> ( ( ph /\ ps ) \/ ( ph /\ ch ) ) ) |
2 |
1
|
orbi1i |
|- ( ( ( ph /\ ( ps \/ ch ) ) \/ ( ps /\ ch ) ) <-> ( ( ( ph /\ ps ) \/ ( ph /\ ch ) ) \/ ( ps /\ ch ) ) ) |
3 |
|
wl-df-3mintru2 |
|- ( cadd ( ph , ps , ch ) <-> if- ( ph , ( ps \/ ch ) , ( ps /\ ch ) ) ) |
4 |
|
animorl |
|- ( ( ps /\ ch ) -> ( ps \/ ch ) ) |
5 |
|
wl-ifpimpr |
|- ( ( ( ps /\ ch ) -> ( ps \/ ch ) ) -> ( if- ( ph , ( ps \/ ch ) , ( ps /\ ch ) ) <-> ( ( ph /\ ( ps \/ ch ) ) \/ ( ps /\ ch ) ) ) ) |
6 |
4 5
|
ax-mp |
|- ( if- ( ph , ( ps \/ ch ) , ( ps /\ ch ) ) <-> ( ( ph /\ ( ps \/ ch ) ) \/ ( ps /\ ch ) ) ) |
7 |
3 6
|
bitri |
|- ( cadd ( ph , ps , ch ) <-> ( ( ph /\ ( ps \/ ch ) ) \/ ( ps /\ ch ) ) ) |
8 |
|
df-3or |
|- ( ( ( ph /\ ps ) \/ ( ph /\ ch ) \/ ( ps /\ ch ) ) <-> ( ( ( ph /\ ps ) \/ ( ph /\ ch ) ) \/ ( ps /\ ch ) ) ) |
9 |
2 7 8
|
3bitr4i |
|- ( cadd ( ph , ps , ch ) <-> ( ( ph /\ ps ) \/ ( ph /\ ch ) \/ ( ps /\ ch ) ) ) |