Theorem f1odm

Description: The domain of a one-to-one onto mapping. (Contributed by NM, 8-Mar-2014)

	Ref	Expression
Assertion	f1odm	$$⊢F:A\underset{1-1\; onto}{⟶}B\to \mathrm{dom}F=A$$

Proof

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