Theorem 0un 4359

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 4121	. 2 ⊢ (∅ ∪ 𝐴) = (𝐴 ∪ ∅)
2		un0 4357	. 2 ⊢ (𝐴 ∪ ∅) = 𝐴
3	1, 2	eqtri 2752	1 ⊢ (∅ ∪ 𝐴) = 𝐴

Syntax hints:   = wceq 1540   ∪ cun 3912  ∅c0 4296

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 2008  ax-8 2111  ax-9 2119  ax-ext 2701

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-v 3449  df-dif 3917  df-un 3919  df-nul 4297

This theorem is referenced by:  nlim2  8454  pwmndid  18863  pwmnd  18864  psdmullem  22052  sltlpss  27819  slelss  27820  mulsrid  28016  mulsproplem5  28023  mulsproplem6  28024  mulsproplem7  28025  mulsproplem8  28026  coprprop  32622  fzodif1  32715  cycpmrn  33100  bj-pr22val  37007  bj-snfromadj  37032  tfsconcat0i  43334  fiiuncl  45059  founiiun0  45184  infxrpnf  45442  prsal  46316  meadjun  46460  caragenuncllem  46510  carageniuncllem1  46519  hoidmvle  46598  iscnrm3rlem1  48928