Theorem f1ofun

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

	Ref	Expression
Assertion	f1ofun	⊢ ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 → Fun 𝐹 )

Proof

Step	Hyp	Ref	Expression
1		f1ofn	⊢ ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 → 𝐹 Fn 𝐴 )
2		fnfun	⊢ ( 𝐹 Fn 𝐴 → Fun 𝐹 )
3	1 2	syl	⊢ ( 𝐹 : 𝐴 –1-1-onto→ 𝐵 → Fun 𝐹 )