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Theorem csbov123 6342
 Description: Move class substitution in and out of an operation. (Contributed by NM, 12-Nov-2005.) (Revised by NM, 23-Aug-2018.)
Assertion
Ref Expression
csbov123

Proof of Theorem csbov123
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 csbeq1 3352 . . . 4
2 csbeq1 3352 . . . . 5
3 csbeq1 3352 . . . . 5
4 csbeq1 3352 . . . . 5
52, 3, 4oveq123d 6329 . . . 4
61, 5eqeq12d 2486 . . 3
7 vex 3034 . . . 4
8 nfcsb1v 3365 . . . . 5
9 nfcsb1v 3365 . . . . 5
10 nfcsb1v 3365 . . . . 5
118, 9, 10nfov 6334 . . . 4
12 csbeq1a 3358 . . . . 5
13 csbeq1a 3358 . . . . 5
14 csbeq1a 3358 . . . . 5
1512, 13, 14oveq123d 6329 . . . 4
167, 11, 15csbief 3374 . . 3
176, 16vtoclg 3093 . 2
18 csbprc 3774 . . 3
19 df-ov 6311 . . . 4
20 csbprc 3774 . . . . . 6
2120fveq1d 5881 . . . . 5
22 0fv 5912 . . . . 5
2321, 22syl6eq 2521 . . . 4
2419, 23syl5req 2518 . . 3
2518, 24eqtrd 2505 . 2
2617, 25pm2.61i 169 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wceq 1452   wcel 1904  cvv 3031  csb 3349  c0 3722  cop 3965  cfv 5589  (class class class)co 6308 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-8 1906  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-nul 4527  ax-pow 4579 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-fal 1458  df-ex 1672  df-nf 1676  df-sb 1806  df-eu 2323  df-mo 2324  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-sbc 3256  df-csb 3350  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-uni 4191  df-br 4396  df-dm 4849  df-iota 5553  df-fv 5597  df-ov 6311 This theorem is referenced by:  csbov  6343  csbov12g  6344  relowlpssretop  31837  rdgeqoa  31843
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