Theorem 0un 4396

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 4158	. 2 ⊢ (∅ ∪ 𝐴) = (𝐴 ∪ ∅)
2		un0 4394	. 2 ⊢ (𝐴 ∪ ∅) = 𝐴
3	1, 2	eqtri 2765	1 ⊢ (∅ ∪ 𝐴) = 𝐴

Syntax hints:   = wceq 1540   ∪ cun 3949  ∅c0 4333

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 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-v 3482  df-dif 3954  df-un 3956  df-nul 4334

This theorem is referenced by:  nlim2  8528  pwmndid  18949  pwmnd  18950  psdmullem  22169  sltlpss  27945  slelss  27946  mulsrid  28139  mulsproplem5  28146  mulsproplem6  28147  mulsproplem7  28148  mulsproplem8  28149  coprprop  32708  fzodif1  32794  cycpmrn  33163  bj-pr22val  37020  bj-snfromadj  37045  metakunt17  42222  tfsconcat0i  43358  fiiuncl  45070  founiiun0  45195  infxrpnf  45457  prsal  46333  meadjun  46477  caragenuncllem  46527  carageniuncllem1  46536  hoidmvle  46615  iscnrm3rlem1  48837