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Theorem cnvuni 5049
 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 5042 . . . 4
2 eluni2 4011 . . . . . . 7
32anbi2i 676 . . . . . 6
4 r19.42v 2854 . . . . . 6
53, 4bitr4i 244 . . . . 5
652exbii 1593 . . . 4
7 elcnv2 5042 . . . . . 6
87rexbii 2722 . . . . 5
9 rexcom4 2967 . . . . 5
10 rexcom4 2967 . . . . . 6
1110exbii 1592 . . . . 5
128, 9, 113bitrri 264 . . . 4
131, 6, 123bitri 263 . . 3
14 eliun 4089 . . 3
1513, 14bitr4i 244 . 2
1615eqriv 2432 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1550   wceq 1652   wcel 1725  wrex 2698  cop 3809  cuni 4007  ciun 4085  ccnv 4869 This theorem is referenced by:  funcnvuni  5510 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-uni 4008  df-iun 4087  df-br 4205  df-opab 4259  df-cnv 4878
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