Theorem 0un 4362

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 4124	. 2 ⊢ (∅ ∪ 𝐴) = (𝐴 ∪ ∅)
2		un0 4360	. 2 ⊢ (𝐴 ∪ ∅) = 𝐴
3	1, 2	eqtri 2753	1 ⊢ (∅ ∪ 𝐴) = 𝐴

Syntax hints:   = wceq 1540   ∪ cun 3915  ∅c0 4299

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 2702

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 2709  df-cleq 2722  df-clel 2804  df-v 3452  df-dif 3920  df-un 3922  df-nul 4300

This theorem is referenced by:  nlim2  8457  pwmndid  18870  pwmnd  18871  psdmullem  22059  sltlpss  27826  slelss  27827  mulsrid  28023  mulsproplem5  28030  mulsproplem6  28031  mulsproplem7  28032  mulsproplem8  28033  coprprop  32629  fzodif1  32722  cycpmrn  33107  bj-pr22val  37014  bj-snfromadj  37039  tfsconcat0i  43341  fiiuncl  45066  founiiun0  45191  infxrpnf  45449  prsal  46323  meadjun  46467  caragenuncllem  46517  carageniuncllem1  46526  hoidmvle  46605  iscnrm3rlem1  48932