Theorem f1odm

Description: The domain of a one-to-one onto mapping. (Contributed by NM, 8-Mar-2014) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)

	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	1	fndmd	$$⊢F:A\underset{1-1\; onto}{⟶}B\to \mathrm{dom}F=A$$