Theorem unisnv 4932

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 3482	. 2 ⊢ 𝑥 ∈ V
2	1	unisn 4931	1 ⊢ ∪ {𝑥} = 𝑥

Syntax hints:   = wceq 1537  {csn 4631  ∪ cuni 4912

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-un 3968  df-ss 3980  df-sn 4632  df-pr 4634  df-uni 4913

This theorem is referenced by:  uniintsn  4990  uniabio  6530  iotauni2  6532  opabiotafun  6989  onuninsuci  7861  en1b  9064  fin1a2lem10  10447  incexclem  15869  sylow2a  19652  1stckgenlem  23577  alexsubALTlem3  24073  ptcmplem2  24077  icccmplem1  24858  unidifsnel  32561  unidifsnne  32562  disjabrex  32602  disjabrexf  32603  fiunelcarsg  34298  carsgclctunlem1  34299  wevgblacfn  35093  fobigcup  35882  mbfresfi  37653