Description: Part of proof of Lemma G in Crawley p. 116, line 19. Show p \/ q = p \/ u. TODO: reformat cdleme0cp to match this, then replace with cdleme0cp . (Contributed by NM, 19-Apr-2013)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | cdlemg3.l | |- .<_ = ( le ` K ) |
|
| cdlemg3.j | |- .\/ = ( join ` K ) |
||
| cdlemg3.m | |- ./\ = ( meet ` K ) |
||
| cdlemg3.a | |- A = ( Atoms ` K ) |
||
| cdlemg3.h | |- H = ( LHyp ` K ) |
||
| cdlemg3.u | |- U = ( ( P .\/ Q ) ./\ W ) |
||
| Assertion | cdlemg3a | |- ( ( ( K e. HL /\ W e. H ) /\ ( P e. A /\ -. P .<_ W ) /\ Q e. A ) -> ( P .\/ Q ) = ( P .\/ U ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | cdlemg3.l | |- .<_ = ( le ` K ) |
|
| 2 | cdlemg3.j | |- .\/ = ( join ` K ) |
|
| 3 | cdlemg3.m | |- ./\ = ( meet ` K ) |
|
| 4 | cdlemg3.a | |- A = ( Atoms ` K ) |
|
| 5 | cdlemg3.h | |- H = ( LHyp ` K ) |
|
| 6 | cdlemg3.u | |- U = ( ( P .\/ Q ) ./\ W ) |
|
| 7 | 1 2 3 4 5 6 | cdleme8 | |- ( ( ( K e. HL /\ W e. H ) /\ ( P e. A /\ -. P .<_ W ) /\ Q e. A ) -> ( P .\/ U ) = ( P .\/ Q ) ) |
| 8 | 7 | eqcomd | |- ( ( ( K e. HL /\ W e. H ) /\ ( P e. A /\ -. P .<_ W ) /\ Q e. A ) -> ( P .\/ Q ) = ( P .\/ U ) ) |