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Theorem ex-uni 28255
 Description: Example for df-uni 4805. 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
StepHypRef Expression
1 prex 5302 . . 3 {1, 3} ∈ V
2 prex 5302 . . 3 {1, 8} ∈ V
31, 2unipr 4821 . 2 {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4 ex-un 28253 . 2 ({1, 3} ∪ {1, 8}) = {1, 3, 8}
53, 4eqtri 2821 1 {{1, 3}, {1, 8}} = {1, 3, 8}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538   ∪ cun 3881  {cpr 4530  {ctp 4532  ∪ cuni 4804  1c1 10545  3c3 11699  8c8 11704 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770  ax-sep 5171  ax-nul 5178  ax-pr 5299 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3444  df-dif 3886  df-un 3888  df-in 3890  df-ss 3900  df-nul 4247  df-sn 4529  df-pr 4531  df-tp 4533  df-uni 4805 This theorem is referenced by: (None)
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