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Theorem csbiebt 3288
 Description: Conversion of implicit substitution to explicit substitution into a class. (Closed theorem version of csbiegf 3292.) (Contributed by NM, 11-Nov-2005.)
Assertion
Ref Expression
csbiebt
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem csbiebt
StepHypRef Expression
1 elex 2965 . 2
2 spsbc 3174 . . . . 5
32adantr 453 . . . 4
4 simpl 445 . . . . 5
5 biimt 327 . . . . . . 7
6 csbeq1a 3260 . . . . . . . 8
76eqeq1d 2445 . . . . . . 7
85, 7bitr3d 248 . . . . . 6
98adantl 454 . . . . 5
10 nfv 1630 . . . . . 6
11 nfnfc1 2576 . . . . . 6
1210, 11nfan 1847 . . . . 5
13 nfcsb1v 3284 . . . . . . 7
1413a1i 11 . . . . . 6
15 simpr 449 . . . . . 6
1614, 15nfeqd 2587 . . . . 5
174, 9, 12, 16sbciedf 3197 . . . 4
183, 17sylibd 207 . . 3
1913a1i 11 . . . . . . . 8
20 id 21 . . . . . . . 8
2119, 20nfeqd 2587 . . . . . . 7
2211, 21nfan1 1846 . . . . . 6
237biimprcd 218 . . . . . . 7
2423adantl 454 . . . . . 6
2522, 24alrimi 1782 . . . . 5
2625ex 425 . . . 4
2726adantl 454 . . 3
2818, 27impbid 185 . 2
291, 28sylan 459 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wal 1550   wceq 1653   wcel 1726  wnfc 2560  cvv 2957  wsbc 3162  csb 3252 This theorem is referenced by:  csbiedf  3289  csbieb  3290  csbiegf  3292 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-v 2959  df-sbc 3163  df-csb 3253
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