Theorem mptrel

Description: The maps-to notation always describes a binary relation. (Contributed by Scott Fenton, 16-Apr-2012)

	Ref	Expression
Assertion	mptrel	⊢ Rel ( 𝑥 ∈ 𝐴 ↦ 𝐵 )

Proof

Step	Hyp	Ref	Expression
1		df-mpt	⊢ ( 𝑥 ∈ 𝐴 ↦ 𝐵 ) = { ⟨ 𝑥 , 𝑦 ⟩ ∣ ( 𝑥 ∈ 𝐴 ∧ 𝑦 = 𝐵 ) }
2	1	relopabiv	⊢ Rel ( 𝑥 ∈ 𝐴 ↦ 𝐵 )