Theorem ex-uni 31032

Description: Example for df-uni 4867. 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 5395	. . 3 ⊢ {1, 3} ∈ V
2		prex 5395	. . 3 ⊢ {1, 8} ∈ V
3	1, 2	unipr 4883	. 2 ⊢ ∪ {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4		ex-un 31030	. 2 ⊢ ({1, 3} ∪ {1, 8}) = {1, 3, 8}
5	3, 4	eqtri 2783	1 ⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8}

This proof depends on syntax axioms:   = wceq 1569   ∪ cun 4149  {cpr 4586  {ctp 4588  ∪ cuni 4866  1c1 11204  3c3 12401  8c8 12406

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040  ax-8 2146  ax-9 2154  ax-ext 2732  ax-sep 5248  ax-pr 5390

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1572  df-ex 1812  df-sb 2099  df-clab 2739  df-cleq 2752  df-clel 2835  df-v 3452  df-ss 3896  df-un 4151  df-sn 4585  df-pr 4587  df-tp 4589  df-uni 4867

This theorem is used by: (None)