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Theorem ex-uni 30446
Description: Example for df-uni 4907. 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 5436 . . 3 {1, 3} ∈ V
2 prex 5436 . . 3 {1, 8} ∈ V
31, 2unipr 4923 . 2 {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4 ex-un 30444 . 2 ({1, 3} ∪ {1, 8}) = {1, 3, 8}
53, 4eqtri 2764 1 {{1, 3}, {1, 8}} = {1, 3, 8}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1539  cun 3948  {cpr 4627  {ctp 4629   cuni 4906  1c1 11157  3c3 12323  8c8 12328
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1794  ax-4 1808  ax-5 1909  ax-6 1966  ax-7 2006  ax-8 2109  ax-9 2117  ax-ext 2707  ax-sep 5295  ax-nul 5305  ax-pr 5431
This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-tru 1542  df-fal 1552  df-ex 1779  df-sb 2064  df-clab 2714  df-cleq 2728  df-clel 2815  df-v 3481  df-dif 3953  df-un 3955  df-ss 3967  df-nul 4333  df-sn 4626  df-pr 4628  df-tp 4630  df-uni 4907
This theorem is referenced by: (None)
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