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Theorem ex-uni 23812
Description: Example for df-uni 4203. 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 4645 . . 3  |-  { 1 ,  3 }  e.  _V
2 prex 4645 . . 3  |-  { 1 ,  8 }  e.  _V
31, 2unipr 4215 . 2  |-  U. { { 1 ,  3 } ,  { 1 ,  8 } }  =  ( { 1 ,  3 }  u.  { 1 ,  8 } )
4 ex-un 23810 . 2  |-  ( { 1 ,  3 }  u.  { 1 ,  8 } )  =  { 1 ,  3 ,  8 }
53, 4eqtri 2483 1  |-  U. { { 1 ,  3 } ,  { 1 ,  8 } }  =  { 1 ,  3 ,  8 }
Colors of variables: wff setvar class
Syntax hints:    = wceq 1370    u. cun 3437   {cpr 3990   {ctp 3992   U.cuni 4202   1c1 9398   3c3 10487   8c8 10492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1710  ax-7 1730  ax-9 1762  ax-10 1777  ax-11 1782  ax-12 1794  ax-13 1955  ax-ext 2432  ax-sep 4524  ax-nul 4532  ax-pr 4642
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1373  df-ex 1588  df-nf 1591  df-sb 1703  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2604  df-ne 2650  df-v 3080  df-dif 3442  df-un 3444  df-in 3446  df-ss 3453  df-nul 3749  df-sn 3989  df-pr 3991  df-tp 3993  df-uni 4203
This theorem is referenced by: (None)
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