Theorem ex-uni 28898

Description: Example for df-uni 4849. 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

Step	Hyp	Ref	Expression
1		prex 5368	. . 3 ⊢ {1, 3} ∈ V
2		prex 5368	. . 3 ⊢ {1, 8} ∈ V
3	1, 2	unipr 4866	. 2 ⊢ ∪ {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4		ex-un 28896	. 2 ⊢ ({1, 3} ∪ {1, 8}) = {1, 3, 8}
5	3, 4	eqtri 2765	1 ⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8}

Syntax hints:   = wceq 1540   ∪ cun 3894  {cpr 4571  {ctp 4573  ∪ cuni 4848  1c1 10942  3c3 12099  8c8 12104

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1912  ax-6 1970  ax-7 2010  ax-8 2107  ax-9 2115  ax-ext 2708  ax-sep 5236  ax-nul 5243  ax-pr 5365

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 845  df-tru 1543  df-fal 1553  df-ex 1781  df-sb 2067  df-clab 2715  df-cleq 2729  df-clel 2815  df-v 3443  df-dif 3899  df-un 3901  df-in 3903  df-ss 3913  df-nul 4267  df-sn 4570  df-pr 4572  df-tp 4574  df-uni 4849

This theorem is referenced by: (None)