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Theorem iuneq2 3667
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 3666 . . 3  C_  C  U_  C_  U_  C
2 ss2iun 3666 . . 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 2957 . . . 4  C 
C_  C  C  C_
54ralbii 2327 . . 3  C  C_  C  C  C_
6 r19.26 2438 . . 3  C_  C  C  C_  C_  C  C  C_
75, 6bitri 173 . 2  C  C_  C  C  C_
8 eqss 2957 . 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 1243  wral 2303    C_ wss 2914   U_ciun 3651
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-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022
This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2308  df-rex 2309  df-v 2556  df-in 2921  df-ss 2928  df-iun 3653
This theorem is referenced by:  iuneq2i  3669  iuneq2dv  3672  dfmptg  5288
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