Theorem vuniex 4535

Description: The union of a setvar is a set. (Contributed by BJ, 3-May-2021.)

Assertion

Ref	Expression
vuniex	⊢ ∪ 𝑥 ∈ V

Proof of Theorem vuniex

Step	Hyp	Ref	Expression
1		vex 2805	. 2 ⊢ 𝑥 ∈ V
2	1	uniex 4534	1 ⊢ ∪ 𝑥 ∈ V

Syntax hints:   ∈ wcel 2202  Vcvv 2802  ∪ cuni 3893

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-13 2204  ax-14 2205  ax-ext 2213  ax-sep 4207  ax-un 4530

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-rex 2516  df-v 2804  df-uni 3894

This theorem is referenced by:  omp1eomlem  7292  distop  14808  epttop  14813  fncld  14821