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Theorem bnj1523 29377
 Description: Technical lemma for bnj1522 29378. This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011.) (New usage is discouraged.)
Hypotheses
Ref Expression
bnj1523.1
bnj1523.2
bnj1523.3
bnj1523.4
bnj1523.5
bnj1523.6
bnj1523.7
bnj1523.8
bnj1523.9
Assertion
Ref Expression
bnj1523
Distinct variable groups:   ,,,   ,,,   ,   ,,   ,,   ,,,   ,   ,,,   ,,,   ,,   ,   ,
Allowed substitution hints:   (,,,,)   (,,,,)   (,,,)   (,,,,)   (,,,)   (,,,,)   (,,)   (,,)   ()   (,)   (,,,)

Proof of Theorem bnj1523
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 bnj1523.5 . 2
2 bnj1523.6 . . 3
3 bnj1523.9 . . . . . . . . . . . . 13
4 bnj1523.7 . . . . . . . . . . . . . 14
5 bnj1523.1 . . . . . . . . . . . . . . . . 17
6 bnj1523.2 . . . . . . . . . . . . . . . . 17
7 bnj1523.3 . . . . . . . . . . . . . . . . 17
8 bnj1523.4 . . . . . . . . . . . . . . . . 17
95, 6, 7, 8bnj60 29368 . . . . . . . . . . . . . . . 16
101, 9bnj835 29065 . . . . . . . . . . . . . . 15
112, 10bnj832 29063 . . . . . . . . . . . . . 14
124, 11bnj835 29065 . . . . . . . . . . . . 13
133, 12bnj835 29065 . . . . . . . . . . . 12
141simp2bi 973 . . . . . . . . . . . . . . 15
152, 14bnj832 29063 . . . . . . . . . . . . . 14
164, 15bnj835 29065 . . . . . . . . . . . . 13
173, 16bnj835 29065 . . . . . . . . . . . 12
18 bnj213 29190 . . . . . . . . . . . . 13
1918a1i 11 . . . . . . . . . . . 12
203simp3bi 974 . . . . . . . . . . . . . . . . 17
2120bnj1211 29106 . . . . . . . . . . . . . . . 16
22 con2b 325 . . . . . . . . . . . . . . . . 17
2322albii 1575 . . . . . . . . . . . . . . . 16
2421, 23sylib 189 . . . . . . . . . . . . . . 15
25 bnj1418 29346 . . . . . . . . . . . . . . . . 17
2625imim1i 56 . . . . . . . . . . . . . . . 16
2726alimi 1568 . . . . . . . . . . . . . . 15
2824, 27syl 16 . . . . . . . . . . . . . 14
2928bnj1142 29097 . . . . . . . . . . . . 13
30 bnj1523.8 . . . . . . . . . . . . . 14
315bnj1309 29328 . . . . . . . . . . . . . . . . . . 19
327, 31bnj1307 29329 . . . . . . . . . . . . . . . . . 18
3332nfcii 2562 . . . . . . . . . . . . . . . . 17
3433nfuni 4013 . . . . . . . . . . . . . . . 16
358, 34nfcxfr 2568 . . . . . . . . . . . . . . 15
3635nfcrii 2564 . . . . . . . . . . . . . 14
3730, 36bnj1534 29161 . . . . . . . . . . . . 13
3829, 18, 37bnj1533 29160 . . . . . . . . . . . 12
3913, 17, 19, 38bnj1536 29162 . . . . . . . . . . 11
4039opeq2d 3983 . . . . . . . . . 10
4140fveq2d 5724 . . . . . . . . 9
425, 6, 7, 8bnj1500 29374 . . . . . . . . . . . . . . 15
431, 42bnj835 29065 . . . . . . . . . . . . . 14
442, 43bnj832 29063 . . . . . . . . . . . . 13
454, 44bnj835 29065 . . . . . . . . . . . 12
4645, 36bnj1529 29376 . . . . . . . . . . 11
473, 46bnj835 29065 . . . . . . . . . 10
4830bnj21 29019 . . . . . . . . . . 11
493simp2bi 973 . . . . . . . . . . 11
5048, 49bnj1213 29107 . . . . . . . . . 10
5147, 50bnj1294 29126 . . . . . . . . 9
521simp3bi 974 . . . . . . . . . . . . . 14
532, 52bnj832 29063 . . . . . . . . . . . . 13
544, 53bnj835 29065 . . . . . . . . . . . 12
55 ax-17 1626 . . . . . . . . . . . 12
5654, 55bnj1529 29376 . . . . . . . . . . 11
573, 56bnj835 29065 . . . . . . . . . 10
5857, 50bnj1294 29126 . . . . . . . . 9
5941, 51, 583eqtr4d 2477 . . . . . . . 8
6030, 36bnj1534 29161 . . . . . . . . . . 11
6160bnj1538 29163 . . . . . . . . . 10
623, 61bnj836 29066 . . . . . . . . 9
6362neneqd 2614 . . . . . . . 8
6459, 63pm2.65i 167 . . . . . . 7
6564nex 1564 . . . . . 6
661simp1bi 972 . . . . . . . . . 10
672, 66bnj832 29063 . . . . . . . . 9
684, 67bnj835 29065 . . . . . . . 8
6948a1i 11 . . . . . . . 8
704simp2bi 973 . . . . . . . . . 10
714simp3bi 974 . . . . . . . . . 10
7230rabeq2i 2945 . . . . . . . . . 10
7370, 71, 72sylanbrc 646 . . . . . . . . 9
74 ne0i 3626 . . . . . . . . 9
7573, 74syl 16 . . . . . . . 8
76 bnj69 29316 . . . . . . . 8
7768, 69, 75, 76syl3anc 1184 . . . . . . 7
7877, 3bnj1209 29105 . . . . . 6
7965, 78mto 169 . . . . 5
8079nex 1564 . . . 4
812simprbi 451 . . . . . 6
8211, 15, 81, 36bnj1542 29165 . . . . 5
835, 6, 7, 8, 1, 2bnj1525 29375 . . . . 5
8482, 4, 83bnj1521 29159 . . . 4
8580, 84mto 169 . . 3
862, 85bnj1541 29164 . 2
871, 86sylbir 205 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359   w3a 936  wal 1549  wex 1550   wceq 1652   wcel 1725  cab 2421   wne 2598  wral 2697  wrex 2698  crab 2701   wss 3312  c0 3620  cop 3809  cuni 4007   class class class wbr 4204   cres 4872   wfn 5441  cfv 5446   c-bnj14 28989   w-bnj15 28993 This theorem is referenced by:  bnj1522  29378 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-13 1727  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-rep 4312  ax-sep 4322  ax-nul 4330  ax-pow 4369  ax-pr 4395  ax-un 4693  ax-reg 7552  ax-inf2 7588 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3or 937  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-eu 2284  df-mo 2285  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-reu 2704  df-rab 2706  df-v 2950  df-sbc 3154  df-csb 3244  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-pss 3328  df-nul 3621  df-if 3732  df-pw 3793  df-sn 3812  df-pr 3813  df-tp 3814  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-mpt 4260  df-tr 4295  df-eprel 4486  df-id 4490  df-po 4495  df-so 4496  df-fr 4533  df-we 4535  df-ord 4576  df-on 4577  df-lim 4578  df-suc 4579  df-om 4838  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-rn 4881  df-res 4882  df-ima 4883  df-iota 5410  df-fun 5448  df-fn 5449  df-f 5450  df-f1 5451  df-fo 5452  df-f1o 5453  df-fv 5454  df-1o 6716  df-bnj17 28988  df-bnj14 28990  df-bnj13 28992  df-bnj15 28994  df-bnj18 28996  df-bnj19 28998
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