Metamath Proof Explorer

Theorem xpexd

Description: The Cartesian product of two sets is a set. (Contributed by Glauco Siliprandi, 26-Jun-2021)

Ref Expression
Hypotheses xpexd.1 φ A V
xpexd.2 φ B W
Assertion xpexd φ A × B V


Step Hyp Ref Expression
1 xpexd.1 φ A V
2 xpexd.2 φ B W
3 xpexg A V B W A × B V
4 1 2 3 syl2anc φ A × B V