Theorem f1ofun

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

	Ref	Expression
Assertion	f1ofun	$$⊢F:A\underset{1-1\; onto}{⟶}B\to \mathrm{Fun}F$$

Proof

Step	Hyp	Ref	Expression
1		f1ofn	$$⊢F:A\underset{1-1\; onto}{⟶}B\to FFnA$$
2		fnfun	$$⊢FFnA\to \mathrm{Fun}F$$
3	1 2	syl	$$⊢F:A\underset{1-1\; onto}{⟶}B\to \mathrm{Fun}F$$