Theorem ex-uni 31009

Description: Example for df-uni 4868. 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 5396	. . 3 ⊢ {1, 3} ∈ V
2		prex 5396	. . 3 ⊢ {1, 8} ∈ V
3	1, 2	unipr 4884	. 2 ⊢ ∪ {{1, 3}, {1, 8}} = ({1, 3} ∪ {1, 8})
4		ex-un 31007	. 2 ⊢ ({1, 3} ∪ {1, 8}) = {1, 3, 8}
5	3, 4	eqtri 2784	1 ⊢ ∪ {{1, 3}, {1, 8}} = {1, 3, 8}

This proof depends on syntax axioms:   = wceq 1570   ∪ cun 3897  {cpr 4586  {ctp 4588  ∪ cuni 4867  1c1 11182  3c3 12379  8c8 12384

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 2147  ax-9 2155  ax-ext 2733  ax-sep 5249  ax-pr 5391

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 2740  df-cleq 2753  df-clel 2836  df-v 3453  df-un 3904  df-ss 3916  df-sn 4585  df-pr 4587  df-tp 4589  df-uni 4868

This theorem is used by: (None)