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