Theorem bj-resss2

Description: The restriction of a class to a class is included in the Cartesian product of the restricting class with the universal class. (Contributed by BJ, 16-Oct-2026)

	Ref	Expression
Assertion	bj-resss2	$$⊢{R\upharpoonright }_A\subseteq A\times \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		df-res	$$⊢{R\upharpoonright }_A=R\cap \left(A\times \mathrm{V}\right)$$
2		inss2	$$⊢R\cap \left(A\times \mathrm{V}\right)\subseteq A\times \mathrm{V}$$
3	1 2	eqsstri	$$⊢{R\upharpoonright }_A\subseteq A\times \mathrm{V}$$