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Metamath Proof Explorer

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 )