Theorem brresi2

Description: Restriction of a binary relation. (Contributed by Jeff Madsen, 2-Sep-2009)

	Ref	Expression
Hypothesis	brresi2.1	⊢ 𝐵 ∈ V
Assertion	brresi2	⊢ ( 𝐴 ( 𝑅 ↾ 𝐶 ) 𝐵 → 𝐴 𝑅 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		brresi2.1	⊢ 𝐵 ∈ V
2		resss	⊢ ( 𝑅 ↾ 𝐶 ) ⊆ 𝑅
3	2	ssbri	⊢ ( 𝐴 ( 𝑅 ↾ 𝐶 ) 𝐵 → 𝐴 𝑅 𝐵 )