Theorem ex-uni 30174

Description: Example for df-uni 4901. Example by David A. Wheeler. (Contributed by Mario Carneiro, 2-Jul-2016.)

Assertion

Ref	Expression
ex-uni	⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8}

Proof of Theorem ex-uni

Step	Hyp	Ref	Expression
1		prex 5423	. . 3 ⊢ {1, 3} ∈ V
2		prex 5423	. . 3 ⊢ {1, 8} ∈ V
3	1, 2	unipr 4917	. 2 ⊢ ∪ {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4		ex-un 30172	. 2 ⊢ ({1, 3} ∪ {1, 8}) = {1, 3, 8}
5	3, 4	eqtri 2752	1 ⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8}

Syntax hints:   = wceq 1533   ∪ cun 3939  {cpr 4623  {ctp 4625  ∪ cuni 4900  1c1 11108  3c3 12267  8c8 12272

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2695  ax-sep 5290  ax-nul 5297  ax-pr 5418

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2702  df-cleq 2716  df-clel 2802  df-v 3468  df-dif 3944  df-un 3946  df-in 3948  df-ss 3958  df-nul 4316  df-sn 4622  df-pr 4624  df-tp 4626  df-uni 4901

This theorem is referenced by: (None)