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Theorem dalem51 32720
 Description: Lemma for dath 32733. 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 32620 . . . . . 6
323ad2ant1 1018 . . . . 5
4 dalem.ps . . . . . . 7
54dalemccea 32680 . . . . . 6
653ad2ant3 1020 . . . . 5
73, 6jca 530 . . . 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 32693 . . . . 5
17 dalem44.h . . . . . 6
181, 8, 9, 10, 4, 11, 12, 13, 14, 17dalem29 32698 . . . . 5
19 dalem44.i . . . . . 6
201, 8, 9, 10, 4, 11, 12, 13, 14, 19dalem34 32703 . . . . 5
2116, 18, 203jca 1177 . . . 4
221dalempea 32623 . . . . . 6
231dalemqea 32624 . . . . . 6
241dalemrea 32625 . . . . . 6
2522, 23, 243jca 1177 . . . . 5
26253ad2ant1 1018 . . . 4
277, 21, 263jca 1177 . . 3
281, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem42 32711 . . . 4
291dalemyeo 32629 . . . . 5
30293ad2ant1 1018 . . . 4
3128, 30jca 530 . . 3
321, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem45 32714 . . . . 5
331, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem46 32715 . . . . 5
341, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem47 32716 . . . . 5
3532, 33, 343jca 1177 . . . 4
361, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem48 32717 . . . . . 6
371, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem49 32718 . . . . . 6
381, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem50 32719 . . . . . 6
3936, 37, 383jca 1177 . . . . 5
40393adant2 1016 . . . 4
411, 8, 9, 10, 4, 11, 12, 13, 14, 15dalem27 32696 . . . . 5
421, 8, 9, 10, 4, 11, 12, 13, 14, 17dalem32 32701 . . . . 5
431, 8, 9, 10, 4, 11, 12, 13, 14, 19dalem36 32705 . . . . 5
4441, 42, 433jca 1177 . . . 4
4535, 40, 443jca 1177 . . 3
4627, 31, 453jca 1177 . 2
471, 8, 9, 10, 4, 11, 12, 13, 14, 15, 17, 19dalem43 32712 . 2
4846, 47jca 530 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 184   wa 367   w3a 974   wceq 1405   wcel 1842   wne 2598   class class class wbr 4394  cfv 5568  (class class class)co 6277  cbs 14839  cple 14914  cjn 15895  cmee 15896  catm 32261  chlt 32348  clpl 32489 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-8 1844  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-rep 4506  ax-sep 4516  ax-nul 4524  ax-pow 4571  ax-pr 4629  ax-un 6573 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-mo 2243  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2758  df-rex 2759  df-reu 2760  df-rab 2762  df-v 3060  df-sbc 3277  df-csb 3373  df-dif 3416  df-un 3418  df-in 3420  df-ss 3427  df-nul 3738  df-if 3885  df-pw 3956  df-sn 3972  df-pr 3974  df-op 3978  df-uni 4191  df-iun 4272  df-br 4395  df-opab 4453  df-mpt 4454  df-id 4737  df-xp 4828  df-rel 4829  df-cnv 4830  df-co 4831  df-dm 4832  df-rn 4833  df-res 4834  df-ima 4835  df-iota 5532  df-fun 5570  df-fn 5571  df-f 5572  df-f1 5573  df-fo 5574  df-f1o 5575  df-fv 5576  df-riota 6239  df-ov 6280  df-oprab 6281  df-preset 15879  df-poset 15897  df-plt 15910  df-lub 15926  df-glb 15927  df-join 15928  df-meet 15929  df-p0 15991  df-lat 15998  df-clat 16060  df-oposet 32174  df-ol 32176  df-oml 32177  df-covers 32264  df-ats 32265  df-atl 32296  df-cvlat 32320  df-hlat 32349  df-llines 32495  df-lplanes 32496  df-lvols 32497 This theorem is referenced by:  dalem53  32722  dalem54  32723
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