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Theorem bj-uniex2 7139
Description: uniex2 4123 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 7103 . . . 4 BOUNDED 
U.
21bdeli 7073 . . 3 BOUNDED  U.
3 zfun 4121 . . . 4
4 eluni 3557 . . . . . . 7  U.
54imbi1i 227 . . . . . 6  U.
65albii 1339 . . . . 5  U.
76exbii 1478 . . . 4  U.
83, 7mpbir 134 . . 3 
U.
92, 8bdbm1.3ii 7117 . 2  U.
10 dfcleq 2016 . . 3  U.  U.
1110exbii 1478 . 2  U.  U.
129, 11mpbir 134 1  U.
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1226   wceq 1228  wex 1362   wcel 1374   U.cuni 3554
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 617  ax-5 1316  ax-7 1317  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-8 1376  ax-10 1377  ax-11 1378  ax-i12 1379  ax-bnd 1380  ax-4 1381  ax-13 1385  ax-14 1386  ax-17 1400  ax-i9 1404  ax-ial 1409  ax-i5r 1410  ax-ext 2004  ax-un 4120  ax-bd0 7040  ax-bdex 7046  ax-bdel 7048  ax-bdsb 7049  ax-bdsep 7111
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-nf 1330  df-sb 1628  df-clab 2009  df-cleq 2015  df-clel 2018  df-nfc 2149  df-rex 2290  df-v 2537  df-uni 3555  df-bdc 7068
This theorem is referenced by:  bj-uniex  7140
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