Theorem vuniex 4564

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 2818	. 2 ⊢ 𝑥 ∈ V
2	1	uniex 4563	1 ⊢ ∪ 𝑥 ∈ V

Syntax hints:   ∈ wcel 2205  Vcvv 2815  ∪ cuni 3919

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 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-13 2207  ax-14 2208  ax-ext 2216  ax-sep 4233  ax-un 4559

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1812  df-clab 2221  df-cleq 2227  df-clel 2230  df-nfc 2375  df-rex 2528  df-v 2817  df-uni 3920

This theorem is referenced by:  omp1eomlem  7398  distop  15076  epttop  15081  fncld  15089