Theorem f1dm

Description: The domain of a one-to-one mapping. (Contributed by NM, 8-Mar-2014) (Proof shortened by Wolf Lammen, 29-May-2024)

	Ref	Expression
Assertion	f1dm	$$⊢F:A\underset{1-1}{⟶}B\to \mathrm{dom}F=A$$

Proof

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