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Theorem bj-uniexg 11809
Description: uniexg 4265 from bounded separation. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-uniexg (𝐴𝑉 𝐴 ∈ V)

Proof of Theorem bj-uniexg
Dummy variable 𝑥 is distinct from all other variables.
StepHypRef Expression
1 unieq 3662 . . 3 (𝑥 = 𝐴 𝑥 = 𝐴)
21eleq1d 2156 . 2 (𝑥 = 𝐴 → ( 𝑥 ∈ V ↔ 𝐴 ∈ V))
3 vex 2622 . . 3 𝑥 ∈ V
43bj-uniex 11808 . 2 𝑥 ∈ V
52, 4vtoclg 2679 1 (𝐴𝑉 𝐴 ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1289  wcel 1438  Vcvv 2619   cuni 3653
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 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-13 1449  ax-14 1450  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070  ax-un 4260  ax-bd0 11704  ax-bdex 11710  ax-bdel 11712  ax-bdsb 11713  ax-bdsep 11775
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rex 2365  df-v 2621  df-uni 3654  df-bdc 11732
This theorem is referenced by: (None)
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