Theorem relelrni

Description: The second argument of a binary relation belongs to its range. (Contributed by NM, 28-Apr-2015)

	Ref	Expression
Hypothesis	releldm.1	⊢ Rel 𝑅
Assertion	relelrni	⊢ ( 𝐴 𝑅 𝐵 → 𝐵 ∈ ran 𝑅 )

Proof

Step	Hyp	Ref	Expression
1		releldm.1	⊢ Rel 𝑅
2		relelrn	⊢ ( ( Rel 𝑅 ∧ 𝐴 𝑅 𝐵 ) → 𝐵 ∈ ran 𝑅 )
3	1 2	mpan	⊢ ( 𝐴 𝑅 𝐵 → 𝐵 ∈ ran 𝑅 )