Theorem f1fun

Description: A one-to-one mapping is a function. (Contributed by NM, 8-Mar-2014) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)

	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	1	fnfund	⊢ ( 𝐹 : 𝐴 –1-1→ 𝐵 → Fun 𝐹 )