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Metamath Proof Explorer

Theorem f1ofun

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

		Ref	Expression
	Assertion	f1ofun	$⊢ F : A \underset{1-1 onto}{⟶} B \to Fun F$

Step	Hyp	Ref	Expression
1		f1ofn	$⊢ F : A \underset{1-1 onto}{⟶} B \to F Fn A$
2		fnfun	$⊢ F Fn A \to Fun F$
3	1 2	syl	$⊢ F : A \underset{1-1 onto}{⟶} B \to Fun F$