Theorem ex-uni 31057

Description: Example for df-uni 4871. 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 5400	. . 3 ⊢ {1, 3} ∈ V
2		prex 5400	. . 3 ⊢ {1, 8} ∈ V
3	1, 2	unipr 4887	. 2 ⊢ ∪ {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4		ex-un 31055	. 2 ⊢ ({1, 3} ∪ {1, 8}) = {1, 3, 8}
5	3, 4	eqtri 2786	1 ⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8}

This proof depends on syntax axioms:   = wceq 1570   ∪ cun 4152  {cpr 4590  {ctp 4592  ∪ cuni 4870  1c1 11228  3c3 12425  8c8 12430

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 1945  ax-6 2002  ax-7 2043  ax-8 2149  ax-9 2157  ax-ext 2735  ax-sep 5252  ax-pr 5395

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-tru 1573  df-ex 1813  df-sb 2102  df-clab 2742  df-cleq 2755  df-clel 2839  df-v 3456  df-ss 3901  df-un 4154  df-sn 4589  df-pr 4591  df-tp 4593  df-uni 4871

This theorem is used by: (None)