Theorem ex-uni 30249

Description: Example for df-uni 4909. 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 5434	. . 3 ⊢ {1, 3} ∈ V
2		prex 5434	. . 3 ⊢ {1, 8} ∈ V
3	1, 2	unipr 4925	. 2 ⊢ ∪ {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4		ex-un 30247	. 2 ⊢ ({1, 3} ∪ {1, 8}) = {1, 3, 8}
5	3, 4	eqtri 2756	1 ⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8}

Syntax hints:   = wceq 1534   ∪ cun 3945  {cpr 4631  {ctp 4633  ∪ cuni 4908  1c1 11140  3c3 12299  8c8 12304

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1790  ax-4 1804  ax-5 1906  ax-6 1964  ax-7 2004  ax-8 2101  ax-9 2109  ax-ext 2699  ax-sep 5299  ax-nul 5306  ax-pr 5429

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 847  df-tru 1537  df-fal 1547  df-ex 1775  df-sb 2061  df-clab 2706  df-cleq 2720  df-clel 2806  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4324  df-sn 4630  df-pr 4632  df-tp 4634  df-uni 4909

This theorem is referenced by: (None)