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Theorem ex-uni 26675
Description: Example for df-uni 4373. 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 4836 . . 3 {1, 3} ∈ V
2 prex 4836 . . 3 {1, 8} ∈ V
31, 2unipr 4385 . 2 {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4 ex-un 26673 . 2 ({1, 3} ∪ {1, 8}) = {1, 3, 8}
53, 4eqtri 2632 1 {{1, 3}, {1, 8}} = {1, 3, 8}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1475  cun 3538  {cpr 4127  {ctp 4129   cuni 4372  1c1 9816  3c3 10948  8c8 10953
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922  ax-9 1986  ax-10 2006  ax-11 2021  ax-12 2034  ax-13 2234  ax-ext 2590  ax-sep 4709  ax-nul 4717  ax-pr 4833
This theorem depends on definitions:  df-bi 196  df-or 384  df-an 385  df-tru 1478  df-ex 1696  df-nf 1701  df-sb 1868  df-clab 2597  df-cleq 2603  df-clel 2606  df-nfc 2740  df-v 3175  df-dif 3543  df-un 3545  df-in 3547  df-ss 3554  df-nul 3875  df-sn 4126  df-pr 4128  df-tp 4130  df-uni 4373
This theorem is referenced by: (None)
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