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Theorem csbiebt 3454
Description: Conversion of implicit substitution to explicit substitution into a class. (Closed theorem version of csbiegf 3458.) (Contributed by NM, 11-Nov-2005.)
Assertion
Ref Expression
csbiebt
Distinct variable group:   ,

Proof of Theorem csbiebt
StepHypRef Expression
1 elex 3118 . 2
2 spsbc 3340 . . . . 5
32adantr 465 . . . 4
4 simpl 457 . . . . 5
5 biimt 335 . . . . . . 7
6 csbeq1a 3443 . . . . . . . 8
76eqeq1d 2459 . . . . . . 7
85, 7bitr3d 255 . . . . . 6
98adantl 466 . . . . 5
10 nfv 1707 . . . . . 6
11 nfnfc1 2622 . . . . . 6
1210, 11nfan 1928 . . . . 5
13 nfcsb1v 3450 . . . . . . 7
1413a1i 11 . . . . . 6
15 simpr 461 . . . . . 6
1614, 15nfeqd 2626 . . . . 5
174, 9, 12, 16sbciedf 3363 . . . 4
183, 17sylibd 214 . . 3
1913a1i 11 . . . . . . . 8
20 id 22 . . . . . . . 8
2119, 20nfeqd 2626 . . . . . . 7
2211, 21nfan1 1927 . . . . . 6
237biimprcd 225 . . . . . . 7
2423adantl 466 . . . . . 6
2522, 24alrimi 1877 . . . . 5
2625ex 434 . . . 4
2726adantl 466 . . 3
2818, 27impbid 191 . 2
291, 28sylan 471 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818  F/_wnfc 2605   cvv 3109  [.wsbc 3327  [_csb 3434
This theorem is referenced by:  csbiedf  3455  csbieb  3456  csbiegf  3458
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111  df-sbc 3328  df-csb 3435
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