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Theorem ex-uni 25445
Description: Example for df-uni 4191. 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 4632 . . 3  |-  { 1 ,  3 }  e.  _V
2 prex 4632 . . 3  |-  { 1 ,  8 }  e.  _V
31, 2unipr 4203 . 2  |-  U. { { 1 ,  3 } ,  { 1 ,  8 } }  =  ( { 1 ,  3 }  u.  { 1 ,  8 } )
4 ex-un 25443 . 2  |-  ( { 1 ,  3 }  u.  { 1 ,  8 } )  =  { 1 ,  3 ,  8 }
53, 4eqtri 2431 1  |-  U. { { 1 ,  3 } ,  { 1 ,  8 } }  =  { 1 ,  3 ,  8 }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1405    u. cun 3411   {cpr 3973   {ctp 3975   U.cuni 4190   1c1 9443   3c3 10547   8c8 10552
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-sep 4516  ax-nul 4524  ax-pr 4629
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-v 3060  df-dif 3416  df-un 3418  df-in 3420  df-ss 3427  df-nul 3738  df-sn 3972  df-pr 3974  df-tp 3976  df-uni 4191
This theorem is referenced by: (None)
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