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Theorem cnvuni 4521
 Description: The converse of a class union is the (indexed) union of the converses of its members. (Contributed by NM, 11-Aug-2004.)
Assertion
Ref Expression
cnvuni
Distinct variable group:   ,

Proof of Theorem cnvuni
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 elcnv2 4513 . . . 4
2 eluni2 3584 . . . . . . 7
32anbi2i 430 . . . . . 6
4 r19.42v 2467 . . . . . 6
53, 4bitr4i 176 . . . . 5
652exbii 1497 . . . 4
7 elcnv2 4513 . . . . . 6
87rexbii 2331 . . . . 5
9 rexcom4 2577 . . . . 5
10 rexcom4 2577 . . . . . 6
1110exbii 1496 . . . . 5
128, 9, 113bitrri 196 . . . 4
131, 6, 123bitri 195 . . 3
14 eliun 3661 . . 3
1513, 14bitr4i 176 . 2
1615eqriv 2037 1
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243  wex 1381   wcel 1393  wrex 2307  cop 3378  cuni 3580  ciun 3657  ccnv 4344 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-rex 2312  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-uni 3581  df-iun 3659  df-br 3765  df-opab 3819  df-cnv 4353 This theorem is referenced by:  funcnvuni  4968
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