Theorem unisnv 4867

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 3441	. 2 ⊢ 𝑥 ∈ V
2	1	unisn 4866	1 ⊢ ∪ {𝑥} = 𝑥

Syntax hints:   = wceq 1539  {csn 4565  ∪ cuni 4844

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 1911  ax-6 1969  ax-7 2009  ax-8 2106  ax-9 2114  ax-ext 2707

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 846  df-tru 1542  df-ex 1780  df-sb 2066  df-clab 2714  df-cleq 2728  df-clel 2814  df-v 3439  df-un 3897  df-in 3899  df-ss 3909  df-sn 4566  df-pr 4568  df-uni 4845

This theorem is referenced by:  uniintsn  4925  uniabio  6425  iotauni2  6427  opabiotafun  6881  onuninsuci  7719  en1b  8848  fin1a2lem10  10211  incexclem  15593  sylow2a  19269  1stckgenlem  22749  alexsubALTlem3  23245  ptcmplem2  23249  icccmplem1  24030  unidifsnel  30928  unidifsnne  30929  disjabrex  30966  disjabrexf  30967  fiunelcarsg  32328  carsgclctunlem1  32329  fobigcup  34247  mbfresfi  35867