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 3479	. 2 ⊢ 𝑥 ∈ V
2	1	unisn 4931	1 ⊢ ∪ {𝑥} = 𝑥

Syntax hints:   = wceq 1542  {csn 4629  ∪ cuni 4909

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704

This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3477  df-un 3954  df-in 3956  df-ss 3966  df-sn 4630  df-pr 4632  df-uni 4910

This theorem is referenced by:  uniintsn  4992  uniabio  6511  iotauni2  6513  opabiotafun  6973  onuninsuci  7829  en1b  9023  fin1a2lem10  10404  incexclem  15782  sylow2a  19487  1stckgenlem  23057  alexsubALTlem3  23553  ptcmplem2  23557  icccmplem1  24338  unidifsnel  31803  unidifsnne  31804  disjabrex  31844  disjabrexf  31845  fiunelcarsg  33346  carsgclctunlem1  33347  fobigcup  34903  mbfresfi  36582