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Theorem ex-uni 27515
 Description: Example for df-uni 4545. 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 5014 . . 3 {1, 3} ∈ V
2 prex 5014 . . 3 {1, 8} ∈ V
31, 2unipr 4557 . 2 {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4 ex-un 27513 . 2 ({1, 3} ∪ {1, 8}) = {1, 3, 8}
53, 4eqtri 2746 1 {{1, 3}, {1, 8}} = {1, 3, 8}
 Colors of variables: wff setvar class Syntax hints:   = wceq 1596   ∪ cun 3678  {cpr 4287  {ctp 4289  ∪ cuni 4544  1c1 10050  3c3 11184  8c8 11189 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1835  ax-4 1850  ax-5 1952  ax-6 2018  ax-7 2054  ax-9 2112  ax-10 2132  ax-11 2147  ax-12 2160  ax-13 2355  ax-ext 2704  ax-sep 4889  ax-nul 4897  ax-pr 5011 This theorem depends on definitions:  df-bi 197  df-or 384  df-an 385  df-tru 1599  df-ex 1818  df-nf 1823  df-sb 2011  df-clab 2711  df-cleq 2717  df-clel 2720  df-nfc 2855  df-v 3306  df-dif 3683  df-un 3685  df-in 3687  df-ss 3694  df-nul 4024  df-sn 4286  df-pr 4288  df-tp 4290  df-uni 4545 This theorem is referenced by: (None)
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