Metamath Proof Explorer

Theorem xpex

Description: The Cartesian product of two sets is a set. Proposition 6.2 of TakeutiZaring p. 23. (Contributed by NM, 14-Aug-1994)

Ref Expression
Hypotheses xpex.1 
|- A e. _V
xpex.2 
|- B e. _V
Assertion xpex 
|- ( A X. B ) e. _V

Proof

Step Hyp Ref Expression
1 xpex.1 
 |-  A e. _V
2 xpex.2 
 |-  B e. _V
3 xpexg 
 |-  ( ( A e. _V /\ B e. _V ) -> ( A X. B ) e. _V )
4 1 2 3 mp2an 
 |-  ( A X. B ) e. _V