Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bj-uniexg GIF version

Theorem bj-uniexg 10976
Description: uniexg 4221 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 3630 . . 3 (𝑥 = 𝐴 𝑥 = 𝐴)
21eleq1d 2151 . 2 (𝑥 = 𝐴 → ( 𝑥 ∈ V ↔ 𝐴 ∈ V))
3 vex 2613 . . 3 𝑥 ∈ V
43bj-uniex 10975 . 2 𝑥 ∈ V
52, 4vtoclg 2667 1 (𝐴𝑉 𝐴 ∈ V)
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1285  wcel 1434  Vcvv 2610   cuni 3621
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 2065  ax-un 4216  ax-bd0 10871  ax-bdex 10877  ax-bdel 10879  ax-bdsb 10880  ax-bdsep 10942
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-rex 2359  df-v 2612  df-uni 3622  df-bdc 10899
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator