Theorem 0un 4326

Description: The union of the empty set with a class is itself. (Contributed by Glauco Siliprandi, 17-Aug-2020.)

Assertion

Ref	Expression
0un	⊢ (∅ ∪ 𝐴) = 𝐴

Proof of Theorem 0un

Step	Hyp	Ref	Expression
1		uncom 4087	. 2 ⊢ (∅ ∪ 𝐴) = (𝐴 ∪ ∅)
2		un0 4324	. 2 ⊢ (𝐴 ∪ ∅) = 𝐴
3	1, 2	eqtri 2766	1 ⊢ (∅ ∪ 𝐴) = 𝐴

Syntax hints:   = wceq 1539   ∪ cun 3885  ∅c0 4256

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1542  df-fal 1552  df-ex 1783  df-sb 2068  df-clab 2716  df-cleq 2730  df-clel 2816  df-v 3434  df-dif 3890  df-un 3892  df-nul 4257

This theorem is referenced by:  nlim2  8320  pwmndid  18575  pwmnd  18576  coprprop  31032  fzodif1  31114  cycpmrn  31410  sltlpss  34087  bj-pr22val  35209  metakunt17  40141  fiiuncl  42613  founiiun0  42728  infxrpnf  42986  prsal  43859  meadjun  44000  caragenuncllem  44050  carageniuncllem1  44059  hoidmvle  44138  iscnrm3rlem1  46234