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Theorem bnj1463 29361
 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
bnj1463.1
bnj1463.2
bnj1463.3
bnj1463.4
bnj1463.5
bnj1463.6
bnj1463.7
bnj1463.8
bnj1463.9
bnj1463.10
bnj1463.11
bnj1463.12
bnj1463.13
bnj1463.14
bnj1463.15
bnj1463.16
bnj1463.17
bnj1463.18
Assertion
Ref Expression
bnj1463
Distinct variable groups:   ,,,   ,   ,,   ,,,,   ,   ,,,   ,   ,,
Allowed substitution hints:   (,,,,)   (,,,,)   (,,,,)   (,)   (,,,)   (,,,,)   (,,,,)   (,,,,)   (,,,)   (,)   (,,)   ()   (,,,,)   (,,,,)   (,,,)   (,,,,)   (,,,,)

Proof of Theorem bnj1463
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bnj1463.18 . . . . . . 7
2 elex 2956 . . . . . . 7
31, 2syl 16 . . . . . 6
4 eleq1 2495 . . . . . . . 8
5 fneq2 5527 . . . . . . . . 9
6 raleq 2896 . . . . . . . . 9
75, 6anbi12d 692 . . . . . . . 8
84, 7anbi12d 692 . . . . . . 7
9 bnj1463.1 . . . . . . . . . . . 12
109bnj1317 29130 . . . . . . . . . . 11
1110nfcii 2562 . . . . . . . . . 10
1211nfel2 2583 . . . . . . . . 9
13 bnj1463.2 . . . . . . . . . . . . 13
14 bnj1463.3 . . . . . . . . . . . . 13
15 bnj1463.4 . . . . . . . . . . . . 13
16 bnj1463.5 . . . . . . . . . . . . 13
17 bnj1463.6 . . . . . . . . . . . . 13
18 bnj1463.7 . . . . . . . . . . . . 13
19 bnj1463.8 . . . . . . . . . . . . 13
20 bnj1463.9 . . . . . . . . . . . . 13
21 bnj1463.10 . . . . . . . . . . . . 13
22 bnj1463.11 . . . . . . . . . . . . 13
23 bnj1463.12 . . . . . . . . . . . . 13
249, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23bnj1467 29360 . . . . . . . . . . . 12
2524nfcii 2562 . . . . . . . . . . 11
26 nfcv 2571 . . . . . . . . . . 11
2725, 26nffn 5533 . . . . . . . . . 10
28 bnj1463.13 . . . . . . . . . . . . 13
299, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 28bnj1446 29351 . . . . . . . . . . . 12
3029nfi 1560 . . . . . . . . . . 11
3126, 30nfral 2751 . . . . . . . . . 10
3227, 31nfan 1846 . . . . . . . . 9
3312, 32nfan 1846 . . . . . . . 8
3433nfri 1778 . . . . . . 7
35 bnj1463.17 . . . . . . . 8
36 bnj1463.16 . . . . . . . 8
371, 35, 36jca32 522 . . . . . . 7
388, 34, 37bnj1465 29153 . . . . . 6
393, 38mpdan 650 . . . . 5
40 df-rex 2703 . . . . 5
4139, 40sylibr 204 . . . 4
42 bnj1463.15 . . . . 5
43 nfcv 2571 . . . . . . . 8
449, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23bnj1466 29359 . . . . . . . . . . 11
4544nfcii 2562 . . . . . . . . . 10
46 nfcv 2571 . . . . . . . . . 10
4745, 46nffn 5533 . . . . . . . . 9
489, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 28bnj1448 29353 . . . . . . . . . . 11
4948nfi 1560 . . . . . . . . . 10
5046, 49nfral 2751 . . . . . . . . 9
5147, 50nfan 1846 . . . . . . . 8
5243, 51nfrex 2753 . . . . . . 7
5352nfri 1778 . . . . . 6
5425nfeq2 2582 . . . . . . 7
55 fneq1 5526 . . . . . . . 8
56 fveq1 5719 . . . . . . . . . 10
57 reseq1 5132 . . . . . . . . . . . . 13
5857opeq2d 3983 . . . . . . . . . . . 12
5958, 28syl6eqr 2485 . . . . . . . . . . 11
6059fveq2d 5724 . . . . . . . . . 10
6156, 60eqeq12d 2449 . . . . . . . . 9
6261ralbidv 2717 . . . . . . . 8
6355, 62anbi12d 692 . . . . . . 7
6454, 63rexbid 2716 . . . . . 6
6553, 64, 44bnj1468 29154 . . . . 5
6642, 65syl 16 . . . 4
6741, 66mpbird 224 . . 3
68 fveq2 5720 . . . . . . . 8
69 id 20 . . . . . . . . . . 11
70 bnj602 29223 . . . . . . . . . . . 12
7170reseq2d 5138 . . . . . . . . . . 11
7269, 71opeq12d 3984 . . . . . . . . . 10
7313, 72syl5eq 2479 . . . . . . . . 9
7473fveq2d 5724 . . . . . . . 8
7568, 74eqeq12d 2449 . . . . . . 7
7675cbvralv 2924 . . . . . 6
7776anbi2i 676 . . . . 5
7877rexbii 2722 . . . 4
7978sbcbii 3208 . . 3
8067, 79sylibr 204 . 2
8114bnj1454 29150 . . 3
8242, 81syl 16 . 2
8380, 82mpbird 224 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   wfn 5441  cfv 5446   c-bnj14 28989   w-bnj15 28993   c-bnj18 28995 This theorem is referenced by:  bnj1312  29364 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ral 2702  df-rex 2703  df-rab 2706  df-v 2950  df-sbc 3154  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-br 4205  df-opab 4259  df-xp 4876  df-rel 4877  df-cnv 4878  df-co 4879  df-dm 4880  df-res 4882  df-iota 5410  df-fun 5448  df-fn 5449  df-fv 5454  df-bnj14 28990
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