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Theorem bj-uniex2 8369
Description: uniex2 4112 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 8333 . . . 4 BOUNDED 
U.
21bdeli 8303 . . 3 BOUNDED  U.
3 zfun 4110 . . . 4
4 eluni 3547 . . . . . . 7  U.
54imbi1i 227 . . . . . 6  U.
65albii 1333 . . . . 5  U.
76exbii 1470 . . . 4  U.
83, 7mpbir 134 . . 3 
U.
92, 8bdbm1.3ii 8347 . 2  U.
10 dfcleq 2008 . . 3  U.  U.
1110exbii 1470 . 2  U.  U.
129, 11mpbir 134 1  U.
Colors of variables: wff set class
Syntax hints:   wi 4   wa 97   wb 98  wal 1222   wceq 1224  wex 1355   wcel 1367   U.cuni 3544
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 614  ax-5 1310  ax-7 1311  ax-gen 1312  ax-ie1 1356  ax-ie2 1357  ax-8 1369  ax-10 1370  ax-11 1371  ax-i12 1372  ax-bnd 1373  ax-4 1374  ax-13 1378  ax-14 1379  ax-17 1393  ax-i9 1397  ax-ial 1401  ax-i5r 1402  ax-ext 1996  ax-un 4109  ax-bd0 8270  ax-bdex 8276  ax-bdel 8278  ax-bdsb 8279  ax-bdsep 8341
This theorem depends on definitions:  df-bi 110  df-tru 1227  df-nf 1324  df-sb 1620  df-clab 2001  df-cleq 2007  df-clel 2010  df-nfc 2141  df-rex 2282  df-v 2529  df-uni 3545  df-bdc 8298
This theorem is referenced by:  bj-uniex  8370
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