Theorem f1fun

Description: A one-to-one mapping is a function. (Contributed by NM, 8-Mar-2014)

	Ref	Expression
Assertion	f1fun	⊢ ( 𝐹 : 𝐴 –1-1→ 𝐵 → Fun 𝐹 )

Proof

Step	Hyp	Ref	Expression
1		f1fn	⊢ ( 𝐹 : 𝐴 –1-1→ 𝐵 → 𝐹 Fn 𝐴 )
2		fnfun	⊢ ( 𝐹 Fn 𝐴 → Fun 𝐹 )
3	1 2	syl	⊢ ( 𝐹 : 𝐴 –1-1→ 𝐵 → Fun 𝐹 )