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Theorem 0un 4303
 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
StepHypRef Expression
1 uncom 4083 . 2 (∅ ∪ 𝐴) = (𝐴 ∪ ∅)
2 un0 4301 . 2 (𝐴 ∪ ∅) = 𝐴
31, 2eqtri 2821 1 (∅ ∪ 𝐴) = 𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   ∪ cun 3881  ∅c0 4246 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3444  df-dif 3886  df-un 3888  df-nul 4247 This theorem is referenced by:  pwmndid  18113  pwmnd  18114  coprprop  30503  fzodif1  30586  cycpmrn  30884  bj-pr22val  34606  metakunt17  39517  fiiuncl  41870  founiiun0  41987  infxrpnf  42252  prsal  43128  meadjun  43269  caragenuncllem  43319  carageniuncllem1  43328  hoidmvle  43407
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