Theorem ex-uni 30521

Description: Example for df-uni 4846. 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 5374	. . 3 ⊢ {1, 3} ∈ V
2		prex 5374	. . 3 ⊢ {1, 8} ∈ V
3	1, 2	unipr 4862	. 2 ⊢ ∪ {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4		ex-un 30519	. 2 ⊢ ({1, 3} ∪ {1, 8}) = {1, 3, 8}
5	3, 4	eqtri 2763	1 ⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8}

Syntax hints:   = wceq 1547   ∪ cun 3888  {cpr 4564  {ctp 4566  ∪ cuni 4845  1c1 11037  3c3 12235  8c8 12240

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2712  ax-sep 5225  ax-pr 5369

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-tru 1550  df-ex 1787  df-sb 2074  df-clab 2719  df-cleq 2732  df-clel 2815  df-v 3434  df-un 3895  df-ss 3907  df-sn 4563  df-pr 4565  df-tp 4567  df-uni 4846

This theorem is referenced by: (None)