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Theorem csbexg 4584
 Description: The existence of proper substitution into a class. (Contributed by NM, 10-Nov-2005.) (Revised by NM, 17-Aug-2018.)
Assertion
Ref Expression
csbexg

Proof of Theorem csbexg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-csb 3435 . . 3
2 abid2 2597 . . . . . . . 8
3 elex 3118 . . . . . . . 8
42, 3syl5eqel 2549 . . . . . . 7
54alimi 1633 . . . . . 6
6 spsbc 3340 . . . . . 6
75, 6syl5 32 . . . . 5
87imp 429 . . . 4
9 nfcv 2619 . . . . . 6
109sbcabel 3416 . . . . 5
1110adantr 465 . . . 4
128, 11mpbid 210 . . 3
131, 12syl5eqel 2549 . 2
14 csbprc 3821 . . . 4
15 0ex 4582 . . . 4
1614, 15syl6eqel 2553 . . 3
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  e.wcel 1818  {cab 2442   cvv 3109  [.wsbc 3327  [_csb 3434   c0 3784 This theorem is referenced by:  csbex  4585  abfmpeld  27492 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  ax-nul 4581 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-fal 1401  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-in 3482  df-ss 3489  df-nul 3785