Metamath Proof Explorer

Theorem unex

Description: The union of two sets is a set. Corollary 5.8 of TakeutiZaring p. 16. (Contributed by NM, 1-Jul-1994)

Ref Expression
Hypotheses unex.1 
|- A e. _V
unex.2 
|- B e. _V
Assertion unex 
|- ( A u. B ) e. _V

Proof

Step Hyp Ref Expression
1 unex.1 
 |-  A e. _V
2 unex.2 
 |-  B e. _V
3 1 2 unipr 
 |-  U. { A , B } = ( A u. B )
4 prex 
 |-  { A , B } e. _V
5 4 uniex 
 |-  U. { A , B } e. _V
6 3 5 eqeltrri 
 |-  ( A u. B ) e. _V