Theorem forn

Description: The codomain of an onto function is its range. (Contributed by NM, 3-Aug-1994)

	Ref	Expression
Assertion	forn	$$⊢F:A\underset{onto}{⟶}B\to \mathrm{ran}F=B$$

Proof

Step	Hyp	Ref	Expression
1		df-fo	$$⊢F:A\underset{onto}{⟶}B\leftrightarrow \left(FFnA\wedge \mathrm{ran}F=B\right)$$
2	1	simprbi	$$⊢F:A\underset{onto}{⟶}B\to \mathrm{ran}F=B$$