Theorem f1ofn

Description: A one-to-one onto mapping is function on its domain. (Contributed by NM, 12-Dec-2003)

	Ref	Expression
Assertion	f1ofn	⊢ ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 → 𝐹 Fn 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		f1of	⊢ ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 → 𝐹 : 𝐴 ⟶ 𝐵 )
2	1	ffnd	⊢ ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 → 𝐹 Fn 𝐴 )