Theorem fofn

Description: An onto mapping is a function on its domain. (Contributed by NM, 16-Dec-2008)

	Ref	Expression
Assertion	fofn	⊢ ( 𝐹 : 𝐴 –onto→ 𝐵 → 𝐹 Fn 𝐴 )

Proof

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