Theorem 0un 4346

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 4108	. 2 ⊢ (∅ ∪ 𝐴) = (𝐴 ∪ ∅)
2		un0 4344	. 2 ⊢ (𝐴 ∪ ∅) = 𝐴
3	1, 2	eqtri 2754	1 ⊢ (∅ ∪ 𝐴) = 𝐴

Syntax hints:   = wceq 1541   ∪ cun 3900  ∅c0 4283

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2113  ax-9 2121  ax-ext 2703

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2710  df-cleq 2723  df-clel 2806  df-v 3438  df-dif 3905  df-un 3907  df-nul 4284

This theorem is referenced by:  nlim2  8405  pwmndid  18841  pwmnd  18842  psdmullem  22078  sltlpss  27851  slelss  27852  mulsrid  28050  mulsproplem5  28057  mulsproplem6  28058  mulsproplem7  28059  mulsproplem8  28060  coprprop  32675  fzodif1  32770  cycpmrn  33107  bj-pr22val  37052  bj-snfromadj  37077  tfsconcat0i  43377  fiiuncl  45101  founiiun0  45226  infxrpnf  45483  prsal  46355  meadjun  46499  caragenuncllem  46549  carageniuncllem1  46558  hoidmvle  46637  iscnrm3rlem1  48970