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 unexg 
 |-  ( ( A e. _V /\ B e. _V ) -> ( A u. B ) e. _V )
4 1 2 3 mp2an 
 |-  ( A u. B ) e. _V