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Theorem ex-uni 29412
Description: Example for df-uni 4871. 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 5394 . . 3 {1, 3} ∈ V
2 prex 5394 . . 3 {1, 8} ∈ V
31, 2unipr 4888 . 2 {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4 ex-un 29410 . 2 ({1, 3} ∪ {1, 8}) = {1, 3, 8}
53, 4eqtri 2765 1 {{1, 3}, {1, 8}} = {1, 3, 8}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1542  cun 3913  {cpr 4593  {ctp 4595   cuni 4870  1c1 11059  3c3 12216  8c8 12221
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1914  ax-6 1972  ax-7 2012  ax-8 2109  ax-9 2117  ax-ext 2708  ax-sep 5261  ax-nul 5268  ax-pr 5389
This theorem depends on definitions:  df-bi 206  df-an 398  df-or 847  df-tru 1545  df-fal 1555  df-ex 1783  df-sb 2069  df-clab 2715  df-cleq 2729  df-clel 2815  df-v 3450  df-dif 3918  df-un 3920  df-in 3922  df-ss 3932  df-nul 4288  df-sn 4592  df-pr 4594  df-tp 4596  df-uni 4871
This theorem is referenced by: (None)
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