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Theorem csbrngOLD 5474
Description: Distribute proper substitution through the range of a class. (Contributed by Alan Sare, 10-Nov-2012.) Obsolete as of 23-Aug-2018. Use csbrn 5473 instead. (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
csbrngOLD

Proof of Theorem csbrngOLD
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 csbabgOLD 3856 . . 3
2 sbcexgOLD 3382 . . . . 5
3 sbcel2gOLD 3832 . . . . . 6
43exbidv 1714 . . . . 5
52, 4bitrd 253 . . . 4
65abbidv 2593 . . 3
71, 6eqtrd 2498 . 2
8 dfrn3 5197 . . 3
98csbeq2i 3836 . 2
10 dfrn3 5197 . 2
117, 9, 103eqtr4g 2523 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  =wceq 1395  E.wex 1612  e.wcel 1818  {cab 2442  [.wsbc 3327  [_csb 3434  <.cop 4035  rancrn 5005
This theorem is referenced by:  csbima12gALTOLD  33622  csbima12gALTVD  33697
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-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rab 2816  df-v 3111  df-sbc 3328  df-csb 3435  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-cnv 5012  df-dm 5014  df-rn 5015
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