Metamath Proof Explorer


Theorem f1rel

Description: A one-to-one onto mapping is a relation. (Contributed by NM, 8-Mar-2014) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)

Ref Expression
Assertion f1rel ( 𝐹 : 𝐴 –1-1→ 𝐵 → Rel 𝐹 )

Proof

Step Hyp Ref Expression
1 f1f ⊢ ( 𝐹 : 𝐴 –1-1→ 𝐵 → 𝐹 : 𝐴 ⟶ 𝐵 )
2 1 freld ⊢ ( 𝐹 : 𝐴 –1-1→ 𝐵 → Rel 𝐹 )