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 V
xpex.2 B V
Assertion xpex A × B V


Step Hyp Ref Expression
1 xpex.1 A V
2 xpex.2 B V
3 xpexg A V B V A × B V
4 1 2 3 mp2an A × B V