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Theorem bnj1312 29364
 Description: Technical lemma for bnj60 29368. 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
bnj1312.1
bnj1312.2
bnj1312.3
bnj1312.4
bnj1312.5
bnj1312.6
bnj1312.7
bnj1312.8
bnj1312.9
bnj1312.10
bnj1312.11
bnj1312.12
bnj1312.13
bnj1312.14
Assertion
Ref Expression
bnj1312
Distinct variable groups:   ,,,,,   ,   ,   ,   ,,,,   ,,,,,   ,   ,,,,,   ,   ,   ,   ,
Allowed substitution hints:   (,,,)   (,,,)   (,,,)   (,,,)   (,,,)   (,,,)   (,,,,)   (,,,)   ()   (,,,,)   (,,,,)   (,,,)   (,,,,)   (,,,,)

Proof of Theorem bnj1312
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj1312.5 . . 3
2 bnj1312.6 . . . 4
32simplbi 447 . . . . . . 7
41bnj21 29019 . . . . . . . 8
54a1i 11 . . . . . . 7
62simprbi 451 . . . . . . 7
71bnj1230 29111 . . . . . . . 8
87bnj1228 29317 . . . . . . 7
93, 5, 6, 8syl3anc 1184 . . . . . 6
10 bnj1312.7 . . . . . 6
11 nfv 1629 . . . . . . . . 9
127nfcii 2562 . . . . . . . . . 10
13 nfcv 2571 . . . . . . . . . 10
1412, 13nfne 2689 . . . . . . . . 9
1511, 14nfan 1846 . . . . . . . 8
162, 15nfxfr 1579 . . . . . . 7
1716nfri 1778 . . . . . 6
189, 10, 17bnj1521 29159 . . . . 5
1910simp2bi 973 . . . . 5
201bnj1538 29163 . . . . . 6
21 bnj1312.1 . . . . . . . . 9
22 bnj1312.2 . . . . . . . . 9
23 bnj1312.3 . . . . . . . . 9
24 bnj1312.4 . . . . . . . . 9
25 bnj1312.8 . . . . . . . . 9
26 bnj1312.9 . . . . . . . . 9
27 bnj1312.10 . . . . . . . . 9
28 bnj1312.11 . . . . . . . . 9
29 bnj1312.12 . . . . . . . . 9
3021, 22, 23, 24, 1, 2, 10, 25, 26, 27, 28, 29bnj1489 29362 . . . . . . . 8
31 bnj1312.13 . . . . . . . . . . 11
32 bnj1312.14 . . . . . . . . . . 11
3310, 3bnj835 29065 . . . . . . . . . . . . . 14
3421, 22, 23, 24, 1, 2, 10, 25, 26, 27bnj1384 29338 . . . . . . . . . . . . . 14
3533, 34syl 16 . . . . . . . . . . . . 13
3621, 22, 23, 24, 1, 2, 10, 25, 26, 27bnj1415 29344 . . . . . . . . . . . . 13
3735, 36bnj1422 29146 . . . . . . . . . . . 12
3821, 22, 23, 24, 1, 2, 10, 25, 26, 27, 28, 29, 36bnj1416 29345 . . . . . . . . . . . . . 14
3921, 22, 23, 24, 1, 2, 10, 25, 26, 27, 28, 29, 35, 38, 36bnj1421 29348 . . . . . . . . . . . . 13
4039, 38bnj1422 29146 . . . . . . . . . . . 12
4121, 22, 23, 24, 1, 2, 10, 25, 26, 27, 28, 29, 31, 32, 37, 40bnj1423 29357 . . . . . . . . . . 11
4232fneq2i 5532 . . . . . . . . . . . 12
4340, 42sylibr 204 . . . . . . . . . . 11
4421, 22, 23, 24, 1, 2, 10, 25, 26, 27, 28, 29, 31, 32bnj1452 29358 . . . . . . . . . . 11
4521, 22, 23, 24, 1, 2, 10, 25, 26, 27, 28, 29, 31, 32, 30, 41, 43, 44bnj1463 29361 . . . . . . . . . 10
4645, 38jca 519 . . . . . . . . 9
4721, 22, 23, 24, 1, 2, 10, 25, 26, 27, 28, 29, 46bnj1491 29363 . . . . . . . 8
4830, 47mpdan 650 . . . . . . 7
4948, 24bnj1198 29104 . . . . . 6
5020, 49nsyl3 113 . . . . 5
5118, 19, 50bnj1304 29128 . . . 4
522, 51bnj1541 29164 . . 3
531, 52bnj1476 29155 . 2
5424exbii 1592 . . . 4
55 df-rex 2703 . . . 4
5654, 55bitr4i 244 . . 3
5756ralbii 2721 . 2
5853, 57sylib 189 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wa 359   w3a 936  wex 1550   wceq 1652   wcel 1725  cab 2421   wne 2598  wral 2697  wrex 2698  crab 2701  cvv 2948  wsbc 3153   cun 3310   wss 3312  c0 3620  csn 3806  cop 3809  cuni 4007   class class class wbr 4204   cdm 4870   cres 4872   wfun 5440   wfn 5441  cfv 5446   c-bnj14 28989   w-bnj15 28993   c-bnj18 28995 This theorem is referenced by:  bnj1493  29365 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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