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Theorem iuneq2dv 3669
Description: Equality deduction for indexed union. (Contributed by NM, 3-Aug-2004.)
Hypothesis
Ref Expression
iuneq2dv.1  C
Assertion
Ref Expression
iuneq2dv  U_  U_  C
Distinct variable group:   ,
Allowed substitution hints:   ()   ()    C()

Proof of Theorem iuneq2dv
StepHypRef Expression
1 iuneq2dv.1 . . 3  C
21ralrimiva 2386 . 2  C
3 iuneq2 3664 . 2  C  U_  U_  C
42, 3syl 14 1  U_  U_  C
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wceq 1242   wcel 1390  wral 2300   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-bnd 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:  iuneq12d  3672  iuneq2d  3673  oav2  5982  omv2  5984
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