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Theorem bj-uniex2 9347
Description: uniex2 4139 from bounded separation. (Contributed by BJ, 15-Oct-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-uniex2  U.
Distinct variable group:   ,

Proof of Theorem bj-uniex2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bdcuni 9311 . . . 4 BOUNDED 
U.
21bdeli 9281 . . 3 BOUNDED  U.
3 zfun 4137 . . . 4
4 eluni 3574 . . . . . . 7  U.
54imbi1i 227 . . . . . 6  U.
65albii 1356 . . . . 5  U.
76exbii 1493 . . . 4  U.
83, 7mpbir 134 . . 3 
U.
92, 8bdbm1.3ii 9325 . 2  U.
10 dfcleq 2031 . . 3  U.  U.
1110exbii 1493 . 2  U.  U.
129, 11mpbir 134 1  U.
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1240   wceq 1242  wex 1378   wcel 1390   U.cuni 3571
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-13 1401  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-un 4136  ax-bd0 9248  ax-bdex 9254  ax-bdel 9256  ax-bdsb 9257  ax-bdsep 9319
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-rex 2306  df-v 2553  df-uni 3572  df-bdc 9276
This theorem is referenced by:  bj-uniex  9348
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