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Metamath Proof Explorer

Theorem f1of

Description: A one-to-one onto mapping is a mapping. (Contributed by NM, 12-Dec-2003)

		Ref	Expression
	Assertion	f1of	$⊢ F : A \underset{1-1 onto}{⟶} B \to F : A ⟶ B$

Step	Hyp	Ref	Expression
1		f1of1	$⊢ F : A \underset{1-1 onto}{⟶} B \to F : A \underset{1-1}{⟶} B$
2		f1f	$⊢ F : A \underset{1-1}{⟶} B \to F : A ⟶ B$
3	1 2	syl	$⊢ F : A \underset{1-1 onto}{⟶} B \to F : A ⟶ B$