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Metamath Proof Explorer

Theorem f1oen

Description: The domain and range of a one-to-one, onto function are equinumerous. (Contributed by NM, 19-Jun-1998)

		Ref	Expression
	Hypothesis	f1oen.1	$⊢ A \in V$
	Assertion	f1oen	$⊢ F : A \underset{1-1 onto}{⟶} B \to A \approx B$

Step	Hyp	Ref	Expression
1		f1oen.1	$⊢ A \in V$
2		f1oeng	$⊢ (A \in V \land F : A \underset{1-1 onto}{⟶} B) \to A \approx B$
3	1 2	mpan	$⊢ F : A \underset{1-1 onto}{⟶} B \to A \approx B$