Theorem releldmi

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

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

Proof

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