Theorem unisnv 4891

Description: A set equals the union of its singleton (setvar case). (Contributed by NM, 30-Aug-1993.)

Assertion

Ref	Expression
unisnv	⊢ ∪ {𝑥} = 𝑥

Proof of Theorem unisnv

Step	Hyp	Ref	Expression
1		vex 3451	. 2 ⊢ 𝑥 ∈ V
2	1	unisn 4890	1 ⊢ ∪ {𝑥} = 𝑥

Syntax hints:   = wceq 1540  {csn 4589  ∪ cuni 4871

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3449  df-un 3919  df-ss 3931  df-sn 4590  df-pr 4592  df-uni 4872

This theorem is referenced by:  uniintsn  4949  uniabio  6478  iotauni2  6480  opabiotafun  6941  onuninsuci  7816  en1b  8996  fin1a2lem10  10362  incexclem  15802  sylow2a  19549  1stckgenlem  23440  alexsubALTlem3  23936  ptcmplem2  23940  icccmplem1  24711  unidifsnel  32464  unidifsnne  32465  disjabrex  32511  disjabrexf  32512  fiunelcarsg  34307  carsgclctunlem1  34308  wevgblacfn  35096  fobigcup  35888  mbfresfi  37660  termco  49470