Theorem 0un 4323

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 4083	. 2 ⊢ (∅ ∪ 𝐴) = (𝐴 ∪ ∅)
2		un0 4321	. 2 ⊢ (𝐴 ∪ ∅) = 𝐴
3	1, 2	eqtri 2766	1 ⊢ (∅ ∪ 𝐴) = 𝐴

Syntax hints:   = wceq 1539   ∪ cun 3881  ∅c0 4253

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2110  ax-9 2118  ax-ext 2709

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-tru 1542  df-fal 1552  df-ex 1784  df-sb 2069  df-clab 2716  df-cleq 2730  df-clel 2817  df-v 3424  df-dif 3886  df-un 3888  df-nul 4254

This theorem is referenced by:  pwmndid  18490  pwmnd  18491  coprprop  30934  fzodif1  31016  cycpmrn  31312  sltlpss  34014  bj-pr22val  35136  metakunt17  40069  fiiuncl  42502  founiiun0  42617  infxrpnf  42876  prsal  43749  meadjun  43890  caragenuncllem  43940  carageniuncllem1  43949  hoidmvle  44028  iscnrm3rlem1  46122