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Metamath Proof Explorer

Theorem f1ofo

Description: A one-to-one onto function is an onto function. (Contributed by NM, 28-Apr-2004)

		Ref	Expression
	Assertion	f1ofo	$⊢ F : A \underset{1-1 onto}{⟶} B \to F : A \underset{onto}{⟶} B$

Step	Hyp	Ref	Expression
1		dff1o3	$⊢ F : A \underset{1-1 onto}{⟶} B \leftrightarrow (F : A \underset{onto}{⟶} B \land Fun F^{-1})$
2	1	simplbi	$⊢ F : A \underset{1-1 onto}{⟶} B \to F : A \underset{onto}{⟶} B$