Theorem unisnv 4892

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 3458	. 2 ⊢ 𝑥 ∈ V
2	1	unisn 4891	1 ⊢ ∪ {𝑥} = 𝑥

This proof depends on syntax axioms:   = wceq 1570  {csn 4588  ∪ cuni 4872

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-un 4154  df-sn 4589  df-pr 4591  df-uni 4873

This theorem is used by:  uniintsn  4950  uniabio  6534  iotauni2  6536  opabiotafun  6996  onuninsuci  7885  en1b  9090  fin1a2lem10  10526  incexclem  16049  sylow2a  19884  1stckgenlem  23927  alexsubALTlem3  24423  ptcmplem2  24427  icccmplem1  25197  unidifsnel  33229  unidifsnne  33230  disjabrex  33274  disjabrexf  33275  esplyfval1  34316  fiunelcarsg  35059  carsgclctunlem1  35060  fineqvnttrclselem2  35931  fineqvnttrclse  35933  wevgblacfn  36080  fobigcup  36877  mbfresfi  38852  termco  50947