Theorem relxp

Description: A Cartesian product is a relation. Theorem 3.13(i) of Monk1 p. 37. (Contributed by NM, 2-Aug-1994)

	Ref	Expression
Assertion	relxp	⊢ Rel ( 𝐴 × 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		xpss	⊢ ( 𝐴 × 𝐵 ) ⊆ ( V × V )
2		df-rel	⊢ ( Rel ( 𝐴 × 𝐵 ) ↔ ( 𝐴 × 𝐵 ) ⊆ ( V × V ) )
3	1 2	mpbir	⊢ Rel ( 𝐴 × 𝐵 )