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Theorem bj-uniex2 10865
 Description: uniex2 4199 from bounded separation. (Contributed by BJ, 15-Oct-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-uniex2
Distinct variable group:   ,

Proof of Theorem bj-uniex2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 bdcuni 10825 . . . 4 BOUNDED
21bdeli 10795 . . 3 BOUNDED
3 zfun 4197 . . . 4
4 eluni 3612 . . . . . . 7
54imbi1i 236 . . . . . 6
65albii 1400 . . . . 5
76exbii 1537 . . . 4
83, 7mpbir 144 . . 3
92, 8bdbm1.3ii 10840 . 2
10 dfcleq 2076 . . 3
1110exbii 1537 . 2
129, 11mpbir 144 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283   wceq 1285  wex 1422   wcel 1434  cuni 3609 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-13 1445  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-un 4196  ax-bd0 10762  ax-bdex 10768  ax-bdel 10770  ax-bdsb 10771  ax-bdsep 10833 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-rex 2355  df-v 2604  df-uni 3610  df-bdc 10790 This theorem is referenced by:  bj-uniex  10866
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