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	$$⊢F:A\underset{1-1}{⟶}B\to \mathrm{Fun}F$$

Proof

Step	Hyp	Ref	Expression
1		f1fn	$$⊢F:A\underset{1-1}{⟶}B\to FFnA$$
2	1	fnfund	$$⊢F:A\underset{1-1}{⟶}B\to \mathrm{Fun}F$$