Theorem f1fn

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

	Ref	Expression
Assertion	f1fn	⊢ ( 𝐹 : 𝐴 –1-1→ 𝐵 → 𝐹 Fn 𝐴 )

Proof

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