Theorem 0un 39215

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 3757	. 2 ⊢ (∅ ∪ 𝐴) = (𝐴 ∪ ∅)
2		un0 3967	. 2 ⊢ (𝐴 ∪ ∅) = 𝐴
3	1, 2	eqtri 2644	1 ⊢ (∅ ∪ 𝐴) = 𝐴

Syntax hints:   = wceq 1483   ∪ cun 3572  ∅c0 3915

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-dif 3577  df-un 3579  df-nul 3916

This theorem is referenced by:  fiiuncl  39234  founiiun0  39377  infxrpnf  39674  meadjun  40679  caragenuncllem  40726  carageniuncllem1  40735  hoidmvle  40814