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Theorem 0un 38240
 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 3719 . 2 (∅ ∪ 𝐴) = (𝐴 ∪ ∅)
2 un0 3919 . 2 (𝐴 ∪ ∅) = 𝐴
31, 2eqtri 2632 1 (∅ ∪ 𝐴) = 𝐴
 Colors of variables: wff setvar class Syntax hints:   = wceq 1475   ∪ cun 3538  ∅c0 3874 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590 This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-dif 3543  df-un 3545  df-nul 3875 This theorem is referenced by:  fiiuncl  38259  founiiun0  38372  meadjun  39355  caragenuncllem  39402  carageniuncllem1  39411  hoidmvle  39490
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