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Theorem cdleme11 29709
 Description: Part of proof of Lemma E in [Crawley] p. 113, 1st sentence of 3rd paragraph on p. 114. and represent f(s) and f(t) respectively. Their proof provides no details of our cdleme11a 29699 through cdleme11 29709, so there may be a simpler proof that we have overlooked. (Contributed by NM, 15-Jun-2012.)
Hypotheses
Ref Expression
cdleme12.l
cdleme12.j
cdleme12.m
cdleme12.a
cdleme12.h
cdleme12.u
cdleme12.f
cdleme12.g
Assertion
Ref Expression
cdleme11

Proof of Theorem cdleme11
StepHypRef Expression
1 simp11l 1071 . . . . . . . . 9
2 hllat 28803 . . . . . . . . 9
31, 2syl 17 . . . . . . . 8
4 simp11 990 . . . . . . . . 9
5 simp12l 1073 . . . . . . . . 9
6 simp13l 1075 . . . . . . . . 9
7 cdleme12.l . . . . . . . . . 10
8 cdleme12.j . . . . . . . . . 10
9 cdleme12.m . . . . . . . . . 10
10 cdleme12.a . . . . . . . . . 10
11 cdleme12.h . . . . . . . . . 10
12 cdleme12.u . . . . . . . . . 10
13 eqid 2258 . . . . . . . . . 10
147, 8, 9, 10, 11, 12, 13cdleme0aa 29649 . . . . . . . . 9
154, 5, 6, 14syl3anc 1187 . . . . . . . 8
1613, 8latjidm 14143 . . . . . . . 8
173, 15, 16syl2anc 645 . . . . . . 7
1817oveq2d 5808 . . . . . 6
19 simp33 998 . . . . . . 7
20 simp21l 1077 . . . . . . . . . 10
2113, 10atbase 28729 . . . . . . . . . 10
2220, 21syl 17 . . . . . . . . 9
23 simp22l 1079 . . . . . . . . . 10
2413, 10atbase 28729 . . . . . . . . . 10
2523, 24syl 17 . . . . . . . . 9
2613, 8latjcl 14119 . . . . . . . . 9
273, 22, 25, 26syl3anc 1187 . . . . . . . 8
2813, 7, 8latleeqj2 14133 . . . . . . . 8
293, 15, 27, 28syl3anc 1187 . . . . . . 7
3019, 29mpbid 203 . . . . . 6
3118, 30eqtr2d 2291 . . . . 5
32 simp21 993 . . . . . . . 8
33 cdleme12.f . . . . . . . . 9
347, 8, 9, 10, 11, 12, 33cdleme1 29666 . . . . . . . 8
354, 5, 6, 32, 34syl13anc 1189 . . . . . . 7
36 simp22 994 . . . . . . . 8
37 cdleme12.g . . . . . . . . 9
387, 8, 9, 10, 11, 12, 37cdleme1 29666 . . . . . . . 8
394, 5, 6, 36, 38syl13anc 1189 . . . . . . 7
4035, 39oveq12d 5810 . . . . . 6
4113, 8latj4 14170 . . . . . . 7
423, 22, 25, 15, 15, 41syl122anc 1196 . . . . . 6
4340, 42eqtr4d 2293 . . . . 5
4431, 43eqtr4d 2293 . . . 4
457, 8, 9, 10, 11, 12, 33, 13cdleme1b 29665 . . . . . 6
464, 5, 6, 20, 45syl13anc 1189 . . . . 5
477, 8, 9, 10, 11, 12, 37, 13cdleme1b 29665 . . . . . 6
484, 5, 6, 23, 47syl13anc 1189 . . . . 5
4913, 8latj4 14170 . . . . 5
503, 22, 46, 25, 48, 49syl122anc 1196 . . . 4
5144, 50eqtr2d 2291 . . 3
5213, 8latjcl 14119 . . . . 5
533, 46, 48, 52syl3anc 1187 . . . 4
5413, 7, 8latleeqj2 14133 . . . 4
553, 53, 27, 54syl3anc 1187 . . 3
5651, 55mpbird 225 . 2
57 simp12 991 . . . 4
58 simp13 992 . . . 4
59 simp23l 1081 . . . 4
60 simp31 996 . . . 4
617, 8, 9, 10, 11, 12, 33cdleme3fa 29675 . . . 4
624, 57, 58, 32, 59, 60, 61syl132anc 1205 . . 3
63 simp32 997 . . . 4
647, 8, 9, 10, 11, 12, 37cdleme3fa 29675 . . . 4
654, 57, 58, 36, 59, 63, 64syl132anc 1205 . . 3
667, 8, 9, 10, 11, 12, 33, 37cdleme11l 29708 . . 3
677, 8, 10ps-1 28916 . . 3
681, 62, 65, 66, 20, 23, 67syl132anc 1205 . 2
6956, 68mpbid 203 1
 Colors of variables: wff set class Syntax hints:   wn 5   wi 6   wb 178   wa 360   w3a 939   wceq 1619   wcel 1621   wne 2421   class class class wbr 3997  cfv 4673  (class class class)co 5792  cbs 13111  cple 13178  cjn 14041  cmee 14042  clat 14114  catm 28703  chlt 28790  clh 29423 This theorem is referenced by:  cdleme16  29724 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-13 1625  ax-14 1626  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2239  ax-rep 4105  ax-sep 4115  ax-nul 4123  ax-pow 4160  ax-pr 4186  ax-un 4484 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 941  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-eu 2122  df-mo 2123  df-clab 2245  df-cleq 2251  df-clel 2254  df-nfc 2383  df-ne 2423  df-nel 2424  df-ral 2523  df-rex 2524  df-reu 2525  df-rab 2527  df-v 2765  df-sbc 2967  df-csb 3057  df-dif 3130  df-un 3132  df-in 3134  df-ss 3141  df-nul 3431  df-if 3540  df-pw 3601  df-sn 3620  df-pr 3621  df-op 3623  df-uni 3802  df-iun 3881  df-iin 3882  df-br 3998  df-opab 4052  df-mpt 4053  df-id 4281  df-xp 4675  df-rel 4676  df-cnv 4677  df-co 4678  df-dm 4679  df-rn 4680  df-res 4681  df-ima 4682  df-fun 4683  df-fn 4684  df-f 4685  df-f1 4686  df-fo 4687  df-f1o 4688  df-fv 4689  df-ov 5795  df-oprab 5796  df-mpt2 5797  df-1st 6056  df-2nd 6057  df-iota 6225  df-undef 6264  df-riota 6272  df-poset 14043  df-plt 14055  df-lub 14071  df-glb 14072  df-join 14073  df-meet 14074  df-p0 14108  df-p1 14109  df-lat 14115  df-clat 14177  df-oposet 28616  df-ol 28618  df-oml 28619  df-covers 28706  df-ats 28707  df-atl 28738  df-cvlat 28762  df-hlat 28791  df-lines 28940  df-psubsp 28942  df-pmap 28943  df-padd 29235  df-lhyp 29427
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