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Theorem 0un 4353
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 4114 . 2 (∅ ∪ 𝐴) = (𝐴 ∪ ∅)
2 un0 4351 . 2 (𝐴 ∪ ∅) = 𝐴
31, 2eqtri 2761 1 (∅ ∪ 𝐴) = 𝐴
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  cun 3909  c0 4283
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2704
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2711  df-cleq 2725  df-clel 2811  df-v 3446  df-dif 3914  df-un 3916  df-nul 4284
This theorem is referenced by:  nlim2  8437  pwmndid  18751  pwmnd  18752  sltlpss  27258  mulsrid  27399  coprprop  31660  fzodif1  31743  cycpmrn  32041  bj-pr22val  35536  bj-snfromadj  35561  metakunt17  40639  fiiuncl  43361  founiiun0  43497  infxrpnf  43767  prsal  44645  meadjun  44789  caragenuncllem  44839  carageniuncllem1  44848  hoidmvle  44927  iscnrm3rlem1  47059
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