Metamath Proof Explorer


Theorem f1orel

Description: A one-to-one onto mapping is a relation. (Contributed by NM, 13-Dec-2003)

Ref Expression
Assertion f1orel ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 → Rel 𝐹 )

Proof

Step Hyp Ref Expression
1 f1ofun ⊢ ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 → Fun 𝐹 )
2 funrel ⊢ ( Fun 𝐹 → Rel 𝐹 )
3 1 2 syl ⊢ ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 → Rel 𝐹 )