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Theorem iunss1 3659
Description: Subclass theorem for indexed union. (Contributed by NM, 10-Dec-2004.) (Proof shortened by Andrew Salmon, 25-Jul-2011.)
Assertion
Ref Expression
iunss1 
C_  U_  C  C_ 
U_  C
Distinct variable groups:   ,   ,
Allowed substitution hint:    C()

Proof of Theorem iunss1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssrexv 2999 . . 3 
C_  C  C
2 eliun 3652 . . 3  U_  C  C
3 eliun 3652 . . 3  U_  C  C
41, 2, 33imtr4g 194 . 2 
C_  U_  C  U_  C
54ssrdv 2945 1 
C_  U_  C  C_ 
U_  C
Colors of variables: wff set class
Syntax hints:   wi 4   wcel 1390  wrex 2301    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-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:  iuneq1  3661  iunxdif2  3696
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