Theorem ex-uni 30455

Description: Example for df-uni 4913. 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 5443	. . 3 ⊢ {1, 3} ∈ V
2		prex 5443	. . 3 ⊢ {1, 8} ∈ V
3	1, 2	unipr 4929	. 2 ⊢ ∪ {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4		ex-un 30453	. 2 ⊢ ({1, 3} ∪ {1, 8}) = {1, 3, 8}
5	3, 4	eqtri 2763	1 ⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8}

Syntax hints:   = wceq 1537   ∪ cun 3961  {cpr 4633  {ctp 4635  ∪ cuni 4912  1c1 11154  3c3 12320  8c8 12325

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-sep 5302  ax-nul 5312  ax-pr 5438

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-sn 4632  df-pr 4634  df-tp 4636  df-uni 4913

This theorem is referenced by: (None)