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Theorem csbopabg 4637
 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 3139 . . 3
2 dfsbcq2 3049 . . . 4
32opabbidv 4625 . . 3
41, 3eqeq12d 2367 . 2
5 vex 2862 . . 3
6 nfs1v 2106 . . . 4
76nfopab 4627 . . 3
8 sbequ12 1919 . . . 4
98opabbidv 4625 . . 3
105, 7, 9csbief 3177 . 2
114, 10vtoclg 2914 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1642  wsb 1648   wcel 1710  wsbc 3046  csb 3136  copab 4622 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-sbc 3047  df-csb 3137  df-opab 4623 This theorem is referenced by: (None)
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