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Theorem dalem39 30193
 Description: Lemma for dath 30218. Auxiliary atoms , , and are not colinear. (Contributed by NM, 4-Aug-2012.)
Hypotheses
Ref Expression
dalem.ph
dalem.l
dalem.j
dalem.a
dalem.ps
dalem38.m
dalem38.o
dalem38.y
dalem38.z
dalem38.g
dalem38.h
dalem38.i
Assertion
Ref Expression
dalem39

Proof of Theorem dalem39
StepHypRef Expression
1 dalem.ph . . . . 5
21dalemkehl 30105 . . . 4
41dalemyeo 30114 . . . . 5
543ad2ant1 978 . . . 4
6 dalem.ps . . . . . 6
76dalemccea 30165 . . . . 5
873ad2ant3 980 . . . 4
96dalem-ccly 30167 . . . . 5
1093ad2ant3 980 . . . 4
11 dalem.l . . . . 5
12 dalem.j . . . . 5
13 dalem.a . . . . 5
14 dalem38.o . . . . 5
15 eqid 2404 . . . . 5
1611, 12, 13, 14, 15lvoli3 30059 . . . 4
173, 5, 8, 10, 16syl31anc 1187 . . 3
18 dalem38.m . . . 4
19 dalem38.y . . . 4
20 dalem38.z . . . 4
21 dalem38.i . . . 4
221, 11, 12, 13, 6, 18, 14, 19, 20, 21dalem34 30188 . . 3
23 dalem38.g . . . 4
241, 11, 12, 13, 6, 18, 14, 19, 20, 23dalem23 30178 . . 3
2511, 12, 13, 15lvolnle3at 30064 . . 3
263, 17, 22, 24, 8, 25syl23anc 1191 . 2
27 dalem38.h . . . . . . 7
281, 11, 12, 13, 6, 18, 14, 19, 20, 23, 27, 21dalem38 30192 . . . . . 6
291dalemkelat 30106 . . . . . . . 8
30293ad2ant1 978 . . . . . . 7
311, 11, 12, 13, 6, 18, 14, 19, 20, 27dalem29 30183 . . . . . . . . 9
32 eqid 2404 . . . . . . . . . 10
3332, 12, 13hlatjcl 29849 . . . . . . . . 9
343, 24, 31, 33syl3anc 1184 . . . . . . . 8
3532, 13atbase 29772 . . . . . . . . 9
3622, 35syl 16 . . . . . . . 8
3732, 12latjcl 14434 . . . . . . . 8
3830, 34, 36, 37syl3anc 1184 . . . . . . 7
396, 13dalemcceb 30171 . . . . . . . 8
40393ad2ant3 980 . . . . . . 7
4132, 11, 12latlej2 14445 . . . . . . 7
4230, 38, 40, 41syl3anc 1184 . . . . . 6
431, 14dalemyeb 30131 . . . . . . . 8
44433ad2ant1 978 . . . . . . 7
4532, 12latjcl 14434 . . . . . . . 8
4630, 38, 40, 45syl3anc 1184 . . . . . . 7
4732, 11, 12latjle12 14446 . . . . . . 7
4830, 44, 40, 46, 47syl13anc 1186 . . . . . 6
4928, 42, 48mpbi2and 888 . . . . 5
5012, 13hlatjrot 29855 . . . . . . 7
513, 24, 31, 22, 50syl13anc 1186 . . . . . 6
5251oveq1d 6055 . . . . 5
5349, 52breqtrd 4196 . . . 4