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

Theorem bj-uniexg 9373
 Description: uniexg 4141 from bounded separation. (Contributed by BJ, 13-Nov-2019.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-uniexg (A 𝑉 A V)

Proof of Theorem bj-uniexg
Dummy variable x is distinct from all other variables.
StepHypRef Expression
1 unieq 3580 . . 3 (x = A x = A)
21eleq1d 2103 . 2 (x = A → ( x V ↔ A V))
3 vex 2554 . . 3 x V
43bj-uniex 9372 . 2 x V
52, 4vtoclg 2607 1 (A 𝑉 A V)
 Colors of variables: wff set class Syntax hints:   → wi 4   = wceq 1242   ∈ wcel 1390  Vcvv 2551  ∪ cuni 3571 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bndl 1396  ax-4 1397  ax-13 1401  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-un 4136  ax-bd0 9268  ax-bdex 9274  ax-bdel 9276  ax-bdsb 9277  ax-bdsep 9339 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-rex 2306  df-v 2553  df-uni 3572  df-bdc 9296 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator