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