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Theorem ex-uni 21734
Description: Example for df-uni 4016. 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 4406 . . 3  |-  { 1 ,  3 }  e.  _V
2 prex 4406 . . 3  |-  { 1 ,  8 }  e.  _V
31, 2unipr 4029 . 2  |-  U. { { 1 ,  3 } ,  { 1 ,  8 } }  =  ( { 1 ,  3 }  u.  { 1 ,  8 } )
4 ex-un 21732 . 2  |-  ( { 1 ,  3 }  u.  { 1 ,  8 } )  =  { 1 ,  3 ,  8 }
53, 4eqtri 2456 1  |-  U. { { 1 ,  3 } ,  { 1 ,  8 } }  =  { 1 ,  3 ,  8 }
Colors of variables: wff set class
Syntax hints:    = wceq 1652    u. cun 3318   {cpr 3815   {ctp 3816   U.cuni 4015   1c1 8991   3c3 10050   8c8 10055
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-ne 2601  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-sn 3820  df-pr 3821  df-tp 3822  df-uni 4016
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