Description: Part of proof of Lemma E in Crawley p. 113. (Contributed by NM, 13-Jun-2012) (New usage is discouraged.)
| 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 ) |
||
| cdleme0c.3 | |- V = ( ( P .\/ R ) ./\ W ) |
||
| Assertion | cdleme0dN | |- ( ( ( K e. HL /\ W e. H ) /\ ( P e. A /\ -. P .<_ W ) /\ ( R e. A /\ P =/= R ) ) -> V 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 | cdleme0c.3 | |- V = ( ( P .\/ R ) ./\ W ) |
|
| 8 | 1 2 3 4 5 7 | lhpat2 | |- ( ( ( K e. HL /\ W e. H ) /\ ( P e. A /\ -. P .<_ W ) /\ ( R e. A /\ P =/= R ) ) -> V e. A ) |