Theorem 0un 4402

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 4168	. 2 ⊢ (∅ ∪ 𝐴) = (𝐴 ∪ ∅)
2		un0 4400	. 2 ⊢ (𝐴 ∪ ∅) = 𝐴
3	1, 2	eqtri 2763	1 ⊢ (∅ ∪ 𝐴) = 𝐴

Syntax hints:   = wceq 1537   ∪ cun 3961  ∅c0 4339

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-dif 3966  df-un 3968  df-nul 4340

This theorem is referenced by:  nlim2  8527  pwmndid  18962  pwmnd  18963  psdmullem  22187  sltlpss  27960  slelss  27961  mulsrid  28154  mulsproplem5  28161  mulsproplem6  28162  mulsproplem7  28163  mulsproplem8  28164  coprprop  32714  fzodif1  32801  cycpmrn  33146  bj-pr22val  37002  bj-snfromadj  37027  metakunt17  42203  tfsconcat0i  43335  fiiuncl  45005  founiiun0  45133  infxrpnf  45396  prsal  46274  meadjun  46418  caragenuncllem  46468  carageniuncllem1  46477  hoidmvle  46556  iscnrm3rlem1  48737