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Theorem bj-unex 14531
Description: unex 4440 from bounded separation. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-unex.1  |-  A  e. 
_V
bj-unex.2  |-  B  e. 
_V
Assertion
Ref Expression
bj-unex  |-  ( A  u.  B )  e. 
_V

Proof of Theorem bj-unex
StepHypRef Expression
1 bj-unex.1 . . 3  |-  A  e. 
_V
2 bj-unex.2 . . 3  |-  B  e. 
_V
31, 2unipr 3823 . 2  |-  U. { A ,  B }  =  ( A  u.  B )
4 bj-prexg 14523 . . . 4  |-  ( ( A  e.  _V  /\  B  e.  _V )  ->  { A ,  B }  e.  _V )
51, 2, 4mp2an 426 . . 3  |-  { A ,  B }  e.  _V
65bj-uniex 14529 . 2  |-  U. { A ,  B }  e.  _V
73, 6eqeltrri 2251 1  |-  ( A  u.  B )  e. 
_V
Colors of variables: wff set class
Syntax hints:    e. wcel 2148   _Vcvv 2737    u. cun 3127   {cpr 3593   U.cuni 3809
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-13 2150  ax-14 2151  ax-ext 2159  ax-pr 4208  ax-un 4432  ax-bd0 14425  ax-bdor 14428  ax-bdex 14431  ax-bdeq 14432  ax-bdel 14433  ax-bdsb 14434  ax-bdsep 14496
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-rex 2461  df-v 2739  df-un 3133  df-sn 3598  df-pr 3599  df-uni 3810  df-bdc 14453
This theorem is referenced by:  bdunexb  14532  bj-unexg  14533
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