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 )