Description: The predicate "is an atom". ( elatcv0 analog.) (Contributed by NM, 18-Jun-2012)
Ref | Expression | ||
---|---|---|---|
Hypotheses | isatom.b | |- B = ( Base ` K ) |
|
isatom.z | |- .0. = ( 0. ` K ) |
||
isatom.c | |- C = ( |
||
isatom.a | |- A = ( Atoms ` K ) |
||
Assertion | isat2 | |- ( ( K e. D /\ P e. B ) -> ( P e. A <-> .0. C P ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isatom.b | |- B = ( Base ` K ) |
|
2 | isatom.z | |- .0. = ( 0. ` K ) |
|
3 | isatom.c | |- C = ( |
|
4 | isatom.a | |- A = ( Atoms ` K ) |
|
5 | 1 2 3 4 | isat | |- ( K e. D -> ( P e. A <-> ( P e. B /\ .0. C P ) ) ) |
6 | 5 | baibd | |- ( ( K e. D /\ P e. B ) -> ( P e. A <-> .0. C P ) ) |