Mathbox for Jonathan Ben-Naim < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  bnj1463 Structured version   Visualization version   Unicode version

Theorem bnj1463 29936
 Description: Technical lemma for bnj60 29943. 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 3040 . . . . . . 7
31, 2syl 17 . . . . . 6
4 eleq1 2537 . . . . . . . 8
5 fneq2 5675 . . . . . . . . 9
6 raleq 2973 . . . . . . . . 9
75, 6anbi12d 725 . . . . . . . 8
84, 7anbi12d 725 . . . . . . 7
9 bnj1463.1 . . . . . . . . . . . 12
109bnj1317 29705 . . . . . . . . . . 11
1110nfcii 2603 . . . . . . . . . 10
1211nfel2 2628 . . . . . . . . 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 29935 . . . . . . . . . . . 12
2524nfcii 2603 . . . . . . . . . . 11
26 nfcv 2612 . . . . . . . . . . 11
2725, 26nffn 5682 . . . . . . . . . 10
28 bnj1463.13 . . . . . . . . . . . . 13
299, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 28bnj1446 29926 . . . . . . . . . . . 12
3029nfi 1682 . . . . . . . . . . 11
3126, 30nfral 2789 . . . . . . . . . 10
3227, 31nfan 2031 . . . . . . . . 9
3312, 32nfan 2031 . . . . . . . 8
3433nfri 1972 . . . . . . 7
35 bnj1463.17 . . . . . . . 8
36 bnj1463.16 . . . . . . . 8
371, 35, 36jca32 544 . . . . . . 7
388, 34, 37bnj1465 29728 . . . . . 6
393, 38mpdan 681 . . . . 5
40 df-rex 2762 . . . . 5
4139, 40sylibr 217 . . . 4
42 bnj1463.15 . . . . 5
43 nfcv 2612 . . . . . . . 8
449, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23bnj1466 29934 . . . . . . . . . . 11
4544nfcii 2603 . . . . . . . . . 10
46 nfcv 2612 . . . . . . . . . 10
4745, 46nffn 5682 . . . . . . . . 9
489, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 28bnj1448 29928 . . . . . . . . . . 11
4948nfi 1682 . . . . . . . . . 10
5046, 49nfral 2789 . . . . . . . . 9
5147, 50nfan 2031 . . . . . . . 8
5243, 51nfrex 2848 . . . . . . 7
5352nfri 1972 . . . . . 6
5425nfeq2 2627 . . . . . . 7
55 fneq1 5674 . . . . . . . 8
56 fveq1 5878 . . . . . . . . . 10
57 reseq1 5105 . . . . . . . . . . . . 13
5857opeq2d 4165 . . . . . . . . . . . 12
5958, 28syl6eqr 2523 . . . . . . . . . . 11
6059fveq2d 5883 . . . . . . . . . 10
6156, 60eqeq12d 2486 . . . . . . . . 9
6261ralbidv 2829 . . . . . . . 8
6355, 62anbi12d 725 . . . . . . 7
6454, 63rexbid 2891 . . . . . 6
6553, 64, 44bnj1468 29729 . . . . 5
6642, 65syl 17 . . . 4
6741, 66mpbird 240 . . 3
68 fveq2 5879 . . . . . . . 8
69 id 22 . . . . . . . . . . 11
70 bnj602 29798 . . . . . . . . . . . 12
7170reseq2d 5111 . . . . . . . . . . 11
7269, 71opeq12d 4166 . . . . . . . . . 10
7313, 72syl5eq 2517 . . . . . . . . 9
7473fveq2d 5883 . . . . . . . 8
7568, 74eqeq12d 2486 . . . . . . 7
7675cbvralv 3005 . . . . . 6
7776anbi2i 708 . . . . 5
7877rexbii 2881 . . . 4
7978sbcbii 3311 . . 3
8067, 79sylibr 217 . 2
8114bnj1454 29725 . . 3
8242, 81syl 17 . 2
8380, 82mpbird 240 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 189   wa 376   w3a 1007   wceq 1452  wex 1671   wcel 1904  cab 2457   wne 2641  wral 2756  wrex 2757  crab 2760  cvv 3031  wsbc 3255   cun 3388   wss 3390  c0 3722  csn 3959  cop 3965  cuni 4190   class class class wbr 4395   cdm 4839   cres 4841   wfn 5584  cfv 5589   c-bnj14 29565   w-bnj15 29569   c-bnj18 29571 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-sbc 3256  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-br 4396  df-opab 4455  df-xp 4845  df-rel 4846  df-cnv 4847  df-co 4848  df-dm 4849  df-res 4851  df-iota 5553  df-fun 5591  df-fn 5592  df-fv 5597  df-bnj14 29566 This theorem is referenced by:  bnj1312  29939
 Copyright terms: Public domain W3C validator