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Theorem iuneq2 3664
Description: Equality theorem for indexed union. (Contributed by NM, 22-Oct-2003.)
Assertion
Ref Expression
iuneq2  C  U_  U_  C

Proof of Theorem iuneq2
StepHypRef Expression
1 ss2iun 3663 . . 3  C_  C  U_  C_  U_  C
2 ss2iun 3663 . . 3  C  C_  U_  C  C_  U_
31, 2anim12i 321 . 2  C_  C  C  C_  U_  C_  U_  C  U_  C  C_ 
U_
4 eqss 2954 . . . 4  C 
C_  C  C  C_
54ralbii 2324 . . 3  C  C_  C  C  C_
6 r19.26 2435 . . 3  C_  C  C  C_  C_  C  C  C_
75, 6bitri 173 . 2  C  C_  C  C  C_
8 eqss 2954 . 2  U_  U_  C  U_  C_  U_  C  U_  C  C_ 
U_
93, 7, 83imtr4i 190 1  C  U_  U_  C
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wceq 1242  wral 2300    C_ wss 2911   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:  iuneq2i  3666  iuneq2dv  3669  dfmptg  5285
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