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Theorem bj-uniexg 13146
 Description: uniexg 4361 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 3745 . . 3 (𝑥 = 𝐴 𝑥 = 𝐴)
21eleq1d 2208 . 2 (𝑥 = 𝐴 → ( 𝑥 ∈ V ↔ 𝐴 ∈ V))
3 vex 2689 . . 3 𝑥 ∈ V
43bj-uniex 13145 . 2 𝑥 ∈ V
52, 4vtoclg 2746 1 (𝐴𝑉 𝐴 ∈ V)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1331   ∈ wcel 1480  Vcvv 2686  ∪ cuni 3736 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-13 1491  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-un 4355  ax-bd0 13041  ax-bdex 13047  ax-bdel 13049  ax-bdsb 13050  ax-bdsep 13112 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-rex 2422  df-v 2688  df-uni 3737  df-bdc 13069 This theorem is referenced by: (None)
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