Metamath Proof Explorer

Theorem coex

Description: The composition of two sets is a set. (Contributed by NM, 15-Dec-2003)

Ref Expression
Hypotheses coex.1 
|- A e. _V
coex.2 
|- B e. _V
Assertion coex 
|- ( A o. B ) e. _V

Proof

Step Hyp Ref Expression
1 coex.1 
 |-  A e. _V
2 coex.2 
 |-  B e. _V
3 coexg 
 |-  ( ( A e. _V /\ B e. _V ) -> ( A o. B ) e. _V )
4 1 2 3 mp2an 
 |-  ( A o. B ) e. _V