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Theorem csbunigOLD 4278
 Description: Distribute proper substitution through the union of a class. (Contributed by Alan Sare, 10-Nov-2012.) Obsolete as of 22-Aug-2018. Use csbuni 4277 instead. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
csbunigOLD

Proof of Theorem csbunigOLD
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 csbabgOLD 3856 . . 3
2 sbcexgOLD 3382 . . . . 5
3 sbcangOLD 3371 . . . . . . 7
4 sbcg 3401 . . . . . . . 8
5 sbcel2gOLD 3832 . . . . . . . 8
64, 5anbi12d 710 . . . . . . 7
73, 6bitrd 253 . . . . . 6
87exbidv 1714 . . . . 5
92, 8bitrd 253 . . . 4
109abbidv 2593 . . 3
111, 10eqtrd 2498 . 2
12 df-uni 4250 . . 3
1312csbeq2i 3836 . 2
14 df-uni 4250 . 2
1511, 13, 143eqtr4g 2523 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  /\wa 369  =wceq 1395  E.wex 1612  e.wcel 1818  {cab 2442  [.wsbc 3327  [_csb 3434  U.cuni 4249 This theorem is referenced by:  csbfv12gALTOLD  33621  csbfv12gALTVD  33699 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-or 370  df-an 371  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  df-uni 4250
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