Description: Part of proof of Lemma E in Crawley p. 113. (Contributed by NM, 12-Jun-2012)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | cdleme0.l | |- .<_ = ( le ` K ) |
|
| cdleme0.j | |- .\/ = ( join ` K ) |
||
| cdleme0.m | |- ./\ = ( meet ` K ) |
||
| cdleme0.a | |- A = ( Atoms ` K ) |
||
| cdleme0.h | |- H = ( LHyp ` K ) |
||
| cdleme0.u | |- U = ( ( P .\/ Q ) ./\ W ) |
||
| Assertion | cdleme0a | |- ( ( ( K e. HL /\ W e. H ) /\ ( P e. A /\ -. P .<_ W ) /\ ( Q e. A /\ P =/= Q ) ) -> U e. A ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cdleme0.l | |- .<_ = ( le ` K ) |
|
| 2 | cdleme0.j | |- .\/ = ( join ` K ) |
|
| 3 | cdleme0.m | |- ./\ = ( meet ` K ) |
|
| 4 | cdleme0.a | |- A = ( Atoms ` K ) |
|
| 5 | cdleme0.h | |- H = ( LHyp ` K ) |
|
| 6 | cdleme0.u | |- U = ( ( P .\/ Q ) ./\ W ) |
|
| 7 | 1 2 3 4 5 6 | lhpat2 | |- ( ( ( K e. HL /\ W e. H ) /\ ( P e. A /\ -. P .<_ W ) /\ ( Q e. A /\ P =/= Q ) ) -> U e. A ) |