Theorem ex-uni 30814

Description: Example for df-uni 4878. 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 5414	. . 3 ⊢ {1, 3} ∈ V
2		prex 5414	. . 3 ⊢ {1, 8} ∈ V
3	1, 2	unipr 4894	. 2 ⊢ ∪ {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4		ex-un 30812	. 2 ⊢ ({1, 3} ∪ {1, 8}) = {1, 3, 8}
5	3, 4	eqtri 2789	1 ⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8}

This proof depends on syntax axioms:   = wceq 1570   ∪ cun 3906  {cpr 4596  {ctp 4598  ∪ cuni 4877  1c1 11119  3c3 12314  8c8 12319

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2738  ax-sep 5262  ax-pr 5409

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2100  df-clab 2745  df-cleq 2758  df-clel 2841  df-v 3460  df-un 3913  df-ss 3925  df-sn 4595  df-pr 4597  df-tp 4599  df-uni 4878

This theorem is used by: (None)