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Theorem csbopabgALT 4785
 Description: Move substitution into a class abstraction. Version of csbopab 4784 with a sethood antecedent but depending on fewer axioms. (Contributed by NM, 6-Aug-2007.) (Proof shortened by Mario Carneiro, 17-Nov-2016.) (New usage is discouraged.) (Proof modification is discouraged.)
Assertion
Ref Expression
csbopabgALT
Distinct variable groups:   ,,   ,,

Proof of Theorem csbopabgALT
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 3437 . . 3
2 dfsbcq2 3330 . . . 4
32opabbidv 4515 . . 3
41, 3eqeq12d 2479 . 2
5 vex 3112 . . 3
6 nfs1v 2181 . . . 4
76nfopab 4517 . . 3
8 sbequ12 1992 . . . 4
98opabbidv 4515 . . 3
105, 7, 9csbief 3459 . 2
114, 10vtoclg 3167 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  =wceq 1395  [wsb 1739  e.wcel 1818  [.wsbc 3327  [_csb 3434  {copab 4509 This theorem is referenced by:  csbcnvgALT  5192 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  df-opab 4511
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