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Theorem ex-uni 25876
Description: Example for df-uni 4199. Example by David A. Wheeler. (Contributed by Mario Carneiro, 2-Jul-2016.)
Assertion
Ref Expression
ex-uni  |-  U. { { 1 ,  3 } ,  { 1 ,  8 } }  =  { 1 ,  3 ,  8 }

Proof of Theorem ex-uni
StepHypRef Expression
1 prex 4642 . . 3  |-  { 1 ,  3 }  e.  _V
2 prex 4642 . . 3  |-  { 1 ,  8 }  e.  _V
31, 2unipr 4211 . 2  |-  U. { { 1 ,  3 } ,  { 1 ,  8 } }  =  ( { 1 ,  3 }  u.  { 1 ,  8 } )
4 ex-un 25874 . 2  |-  ( { 1 ,  3 }  u.  { 1 ,  8 } )  =  { 1 ,  3 ,  8 }
53, 4eqtri 2473 1  |-  U. { { 1 ,  3 } ,  { 1 ,  8 } }  =  { 1 ,  3 ,  8 }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1444    u. cun 3402   {cpr 3970   {ctp 3972   U.cuni 4198   1c1 9540   3c3 10660   8c8 10665
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-9 1896  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431  ax-sep 4525  ax-nul 4534  ax-pr 4639
This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-ne 2624  df-v 3047  df-dif 3407  df-un 3409  df-in 3411  df-ss 3418  df-nul 3732  df-sn 3969  df-pr 3971  df-tp 3973  df-uni 4199
This theorem is referenced by: (None)
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