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Metamath Proof Explorer

Theorem forn

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

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

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