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 ↾ 𝐴 ) ⊆ ( 𝐴 × V )

Proof

Step	Hyp	Ref	Expression
1		df-res	⊢ ( 𝑅 ↾ 𝐴 ) = ( 𝑅 ∩ ( 𝐴 × V ) )
2		inss2	⊢ ( 𝑅 ∩ ( 𝐴 × V ) ) ⊆ ( 𝐴 × V )
3	1 2	eqsstri	⊢ ( 𝑅 ↾ 𝐴 ) ⊆ ( 𝐴 × V )