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Theorem bj-unex 12919
Description: unex 4330 from bounded separation. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Hypotheses
Ref Expression
bj-unex.1 𝐴 ∈ V
bj-unex.2 𝐵 ∈ V
Assertion
Ref Expression
bj-unex (𝐴𝐵) ∈ V

Proof of Theorem bj-unex
StepHypRef Expression
1 bj-unex.1 . . 3 𝐴 ∈ V
2 bj-unex.2 . . 3 𝐵 ∈ V
31, 2unipr 3718 . 2 {𝐴, 𝐵} = (𝐴𝐵)
4 bj-prexg 12911 . . . 4 ((𝐴 ∈ V ∧ 𝐵 ∈ V) → {𝐴, 𝐵} ∈ V)
51, 2, 4mp2an 420 . . 3 {𝐴, 𝐵} ∈ V
65bj-uniex 12917 . 2 {𝐴, 𝐵} ∈ V
73, 6eqeltrri 2189 1 (𝐴𝐵) ∈ V
Colors of variables: wff set class
Syntax hints:  wcel 1463  Vcvv 2658  cun 3037  {cpr 3496   cuni 3704
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-13 1474  ax-14 1475  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-pr 4099  ax-un 4323  ax-bd0 12813  ax-bdor 12816  ax-bdex 12819  ax-bdeq 12820  ax-bdel 12821  ax-bdsb 12822  ax-bdsep 12884
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-rex 2397  df-v 2660  df-un 3043  df-sn 3501  df-pr 3502  df-uni 3705  df-bdc 12841
This theorem is referenced by:  bdunexb  12920  bj-unexg  12921
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