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Theorem ex-uni 20813
Description: Example for df-uni 3828. 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 4217 . . 3  |-  { 1 ,  3 }  e.  _V
2 prex 4217 . . 3  |-  { 1 ,  8 }  e.  _V
31, 2unipr 3841 . 2  |-  U. { { 1 ,  3 } ,  { 1 ,  8 } }  =  ( { 1 ,  3 }  u.  { 1 ,  8 } )
4 ex-un 20811 . 2  |-  ( { 1 ,  3 }  u.  { 1 ,  8 } )  =  { 1 ,  3 ,  8 }
53, 4eqtri 2303 1  |-  U. { { 1 ,  3 } ,  { 1 ,  8 } }  =  { 1 ,  3 ,  8 }
Colors of variables: wff set class
Syntax hints:    = wceq 1623    u. cun 3150   {cpr 3641   {ctp 3642   U.cuni 3827   1c1 8738   3c3 9796   8c8 9801
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-sn 3646  df-pr 3647  df-tp 3648  df-uni 3828
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