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Theorem ex-uni 27137
Description: Example for df-uni 4403. Example by David A. Wheeler. (Contributed by Mario Carneiro, 2-Jul-2016.)
Assertion
Ref Expression
ex-uni {{1, 3}, {1, 8}} = {1, 3, 8}

Proof of Theorem ex-uni
StepHypRef Expression
1 prex 4870 . . 3 {1, 3} ∈ V
2 prex 4870 . . 3 {1, 8} ∈ V
31, 2unipr 4415 . 2 {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4 ex-un 27135 . 2 ({1, 3} ∪ {1, 8}) = {1, 3, 8}
53, 4eqtri 2643 1 {{1, 3}, {1, 8}} = {1, 3, 8}
Colors of variables: wff setvar class
Syntax hints:   = wceq 1480  cun 3553  {cpr 4150  {ctp 4152   cuni 4402  1c1 9881  3c3 11015  8c8 11020
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932  ax-9 1996  ax-10 2016  ax-11 2031  ax-12 2044  ax-13 2245  ax-ext 2601  ax-sep 4741  ax-nul 4749  ax-pr 4867
This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1483  df-ex 1702  df-nf 1707  df-sb 1878  df-clab 2608  df-cleq 2614  df-clel 2617  df-nfc 2750  df-v 3188  df-dif 3558  df-un 3560  df-in 3562  df-ss 3569  df-nul 3892  df-sn 4149  df-pr 4151  df-tp 4153  df-uni 4403
This theorem is referenced by: (None)
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