Description: TODO: FIX COMMENT. TODO: Can this be moved up as a stand-alone theorem in ltrn* area? (Contributed by NM, 4-May-2013)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | cdlemg8.l | |- .<_ = ( le ` K ) |
|
| cdlemg8.j | |- .\/ = ( join ` K ) |
||
| cdlemg8.m | |- ./\ = ( meet ` K ) |
||
| cdlemg8.a | |- A = ( Atoms ` K ) |
||
| cdlemg8.h | |- H = ( LHyp ` K ) |
||
| cdlemg8.t | |- T = ( ( LTrn ` K ) ` W ) |
||
| Assertion | cdlemg10b | |- ( ( ( K e. HL /\ W e. H ) /\ ( ( P e. A /\ -. P .<_ W ) /\ ( Q e. A /\ -. Q .<_ W ) ) /\ F e. T ) -> ( ( ( F ` P ) .\/ ( F ` Q ) ) ./\ W ) = ( ( P .\/ Q ) ./\ W ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cdlemg8.l | |- .<_ = ( le ` K ) |
|
| 2 | cdlemg8.j | |- .\/ = ( join ` K ) |
|
| 3 | cdlemg8.m | |- ./\ = ( meet ` K ) |
|
| 4 | cdlemg8.a | |- A = ( Atoms ` K ) |
|
| 5 | cdlemg8.h | |- H = ( LHyp ` K ) |
|
| 6 | cdlemg8.t | |- T = ( ( LTrn ` K ) ` W ) |
|
| 7 | eqid | |- ( ( P .\/ Q ) ./\ W ) = ( ( P .\/ Q ) ./\ W ) |
|
| 8 | 5 6 1 2 4 3 7 | cdlemg2m | |- ( ( ( K e. HL /\ W e. H ) /\ ( ( P e. A /\ -. P .<_ W ) /\ ( Q e. A /\ -. Q .<_ W ) ) /\ F e. T ) -> ( ( ( F ` P ) .\/ ( F ` Q ) ) ./\ W ) = ( ( P .\/ Q ) ./\ W ) ) |