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Metamath Proof Explorer

Theorem f1odm

Description: The domain of a one-to-one onto mapping. (Contributed by NM, 8-Mar-2014)

		Ref	Expression
	Assertion	f1odm	$⊢ F : A \underset{1-1 onto}{⟶} B \to dom F = A$

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