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Theorem dalem51 30694
 Description: Lemma for dath 30707. Construct the condition with , , and in place of , , and respectively. This lets us reuse the special case of Desargues' Theorem where , to eventually prove the case where . (Contributed by NM, 16-Aug-2012.)
Hypotheses
Ref Expression
dalem.ph
dalem.l
dalem.j
dalem.a
dalem.ps
dalem44.m
dalem44.o
dalem44.y
dalem44.z
dalem44.g
dalem44.h
dalem44.i
Assertion
Ref Expression
dalem51

Proof of Theorem dalem51
StepHypRef Expression
1 dalem.ph . . . . . . 7
21dalemkehl 30594 . . . . . 6
323ad2ant1 979 . . . . 5
4 dalem.ps . . . . . . 7
54dalemccea 30654 . . . . . 6
653ad2ant3 981 . . . . 5
73, 6jca 520 . . . 4
8 dalem.l . . . . . 6
9 dalem.j . . . . . 6
10 dalem.a . . . . . 6
11 dalem44.m . . . . . 6
12 dalem44.o . . . . . 6
13 dalem44.y . . . . . 6
14 dalem44.z . . . . . 6
15 dalem44.g . . . . . 6
161, 8, 9, 10, 4, 11, 12, 13, 14, 15dalem23 30667 . . . . 5
17 dalem44.h . . . . . 6
181, 8, 9, 10, 4, 11, 12, 13, 14, 17dalem29 30672 . . . . 5
19 dalem44.i . . . . . 6
201, 8, 9, 10, 4, 11, 12, 13, 14, 19dalem34 30677 . . . . 5
2116, 18, 203jca 1135 . . . 4
221dalempea 30597 . . . . . 6
231dalemqea 30598 . . . . . 6
241dalemrea 30599 . . . . . 6
2522, 23, 243jca 1135 . . . . 5
26253ad2ant1 979 . . . 4
277, 21, 263jca 1135 . . 3
281, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem42 30685 . . . 4
291dalemyeo 30603 . . . . 5
30293ad2ant1 979 . . . 4
3128, 30jca 520 . . 3
321, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem45 30688 . . . . 5
331, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem46 30689 . . . . 5
341, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem47 30690 . . . . 5
3532, 33, 343jca 1135 . . . 4
361, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem48 30691 . . . . . 6
371, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem49 30692 . . . . . 6
381, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem50 30693 . . . . . 6
3936, 37, 383jca 1135 . . . . 5
40393adant2 977 . . . 4
411, 8, 9, 10, 4, 11, 12, 13, 14, 15dalem27 30670 . . . . 5
421, 8, 9, 10, 4, 11, 12, 13, 14, 17dalem32 30675 . . . . 5
431, 8, 9, 10, 4, 11, 12, 13, 14, 19dalem36 30679 . . . . 5
4441, 42, 433jca 1135 . . . 4
4535, 40, 443jca 1135 . . 3
4627, 31, 453jca 1135 . 2
471, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem43 30686 . 2
4846, 47jca 520 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 178   wa 360   w3a 937   wceq 1654   wcel 1728   wne 2606   class class class wbr 4243  cfv 5489  (class class class)co 6117  cbs 13507  cple 13574  cjn 14439  cmee 14440  catm 30235  chlt 30322  clpl 30463 This theorem is referenced by:  dalem53  30696  dalem54  30697 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1628  ax-9 1669  ax-8 1690  ax-13 1730  ax-14 1732  ax-6 1747  ax-7 1752  ax-11 1764  ax-12 1954  ax-ext 2424  ax-rep 4351  ax-sep 4361  ax-nul 4369  ax-pow 4412  ax-pr 4438  ax-un 4736 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1661  df-eu 2292  df-mo 2293  df-clab 2430  df-cleq 2436  df-clel 2439  df-nfc 2568  df-ne 2608  df-nel 2609  df-ral 2717  df-rex 2718  df-reu 2719  df-rab 2721  df-v 2967  df-sbc 3171  df-csb 3271  df-dif 3312  df-un 3314  df-in 3316  df-ss 3323  df-nul 3617  df-if 3768  df-pw 3830  df-sn 3849  df-pr 3850  df-op 3852  df-uni 4045  df-iun 4124  df-br 4244  df-opab 4298  df-mpt 4299  df-id 4533  df-xp 4919  df-rel 4920  df-cnv 4921  df-co 4922  df-dm 4923  df-rn 4924  df-res 4925  df-ima 4926  df-iota 5453  df-fun 5491  df-fn 5492  df-f 5493  df-f1 5494  df-fo 5495  df-f1o 5496  df-fv 5497  df-ov 6120  df-oprab 6121  df-mpt2 6122  df-1st 6385  df-2nd 6386  df-undef 6579  df-riota 6585  df-poset 14441  df-plt 14453  df-lub 14469  df-glb 14470  df-join 14471  df-meet 14472  df-p0 14506  df-lat 14513  df-clat 14575  df-oposet 30148  df-ol 30150  df-oml 30151  df-covers 30238  df-ats 30239  df-atl 30270  df-cvlat 30294  df-hlat 30323  df-llines 30469  df-lplanes 30470  df-lvols 30471
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