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Theorem csbopabg 3876
 Description: Move substitution into a class abstraction. (Contributed by NM, 6-Aug-2007.) (Proof shortened by Mario Carneiro, 17-Nov-2016.)
Assertion
Ref Expression
csbopabg
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,,)   ()   (,,)

Proof of Theorem csbopabg
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 2920 . . 3
2 dfsbcq2 2827 . . . 4
32opabbidv 3864 . . 3
41, 3eqeq12d 2097 . 2
5 vex 2613 . . 3
6 nfs1v 1858 . . . 4
76nfopab 3866 . . 3
8 sbequ12 1696 . . . 4
98opabbidv 3864 . . 3
105, 7, 9csbief 2956 . 2
114, 10vtoclg 2667 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1285   wcel 1434  wsb 1687  wsbc 2824  csb 2917  copab 3858 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-sbc 2825  df-csb 2918  df-opab 3860 This theorem is referenced by:  csbcnvg  4567
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