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Theorem csbov123g 5701
 Description: Move class substitution in and out of an operation. (Contributed by NM, 12-Nov-2005.) (Proof shortened by Mario Carneiro, 5-Dec-2016.)
Assertion
Ref Expression
csbov123g

Proof of Theorem csbov123g
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 2937 . . 3
2 csbeq1 2937 . . . 4
3 csbeq1 2937 . . . 4
4 csbeq1 2937 . . . 4
52, 3, 4oveq123d 5687 . . 3
61, 5eqeq12d 2103 . 2
7 vex 2623 . . 3
8 nfcsb1v 2964 . . . 4
9 nfcsb1v 2964 . . . 4
10 nfcsb1v 2964 . . . 4
118, 9, 10nfov 5693 . . 3
12 csbeq1a 2942 . . . 4
13 csbeq1a 2942 . . . 4
14 csbeq1a 2942 . . . 4
1512, 13, 14oveq123d 5687 . . 3
167, 11, 15csbief 2973 . 2
176, 16vtoclg 2680 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1290   wcel 1439  csb 2934  (class class class)co 5666 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-rex 2366  df-v 2622  df-sbc 2842  df-csb 2935  df-un 3004  df-sn 3456  df-pr 3457  df-op 3459  df-uni 3660  df-br 3852  df-iota 4993  df-fv 5036  df-ov 5669 This theorem is referenced by:  csbov12g  5702
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