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Theorem dfiunv2 3684
Description: Define double indexed union. (Contributed by FL, 6-Nov-2013.)
Assertion
Ref Expression
dfiunv2  U_  U_  C  {  |  C }
Distinct variable groups:   ,   ,   ,   ,   , C
Allowed substitution hints:   (,)   (,)    C(,)

Proof of Theorem dfiunv2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-iun 3650 . . . 4  U_  C  {  |  C }
21a1i 9 . . 3  U_  C  {  |  C }
32iuneq2i 3666 . 2  U_  U_  C  U_  {  |  C }
4 df-iun 3650 . 2  U_  {  |  C }  {  |  {  |  C } }
5 vex 2554 . . . . 5 
_V
6 eleq1 2097 . . . . . 6  C  C
76rexbidv 2321 . . . . 5  C  C
85, 7elab 2681 . . . 4  {  |  C }  C
98rexbii 2325 . . 3  {  |  C }  C
109abbii 2150 . 2  {  |  {  |  C } }  {  |  C }
113, 4, 103eqtri 2061 1  U_  U_  C  {  |  C }
Colors of variables: wff set class
Syntax hints:   wceq 1242   wcel 1390   {cab 2023  wrex 2301   U_ciun 3648
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-ral 2305  df-rex 2306  df-v 2553  df-in 2918  df-ss 2925  df-iun 3650
This theorem is referenced by: (None)
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