Theorem vuniex 4584

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 2824	. 2 ⊢ 𝑥 ∈ V
2	1	uniex 4583	1 ⊢ ∪ 𝑥 ∈ V

This proof depends on syntax axioms:   ∈ wcel 2209  Vcvv 2821  ∪ cuni 3935

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721  ax-5 1500  ax-7 1501  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-8 1557  ax-10 1558  ax-11 1559  ax-i12 1560  ax-bndl 1562  ax-4 1563  ax-17 1579  ax-i9 1583  ax-ial 1587  ax-i5r 1588  ax-14 2212  ax-ext 2220  ax-sep 4249  ax-un 4578

This proof depends on definitions:  df-bi 117  df-tru 1405  df-nf 1514  df-sb 1816  df-clab 2225  df-cleq 2231  df-clel 2234  df-nfc 2381  df-rex 2534  df-v 2823  df-uni 3936

This theorem is used by:  omp1eomlem  7434  distop  15186  epttop  15191  fncld  15199