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Metamath Proof Explorer

Theorem f1o0

Description: One-to-one onto mapping of the empty set. (Contributed by NM, 10-Sep-2004)

		Ref	Expression
	Assertion	f1o0	$⊢ \emptyset : \emptyset \underset{1-1 onto}{⟶} \emptyset$

Step	Hyp	Ref	Expression
1		eqid	$⊢ \emptyset = \emptyset$
2		f1o00	$⊢ \emptyset : \emptyset \underset{1-1 onto}{⟶} \emptyset \leftrightarrow (\emptyset = \emptyset \land \emptyset = \emptyset)$
3	1 1 2	mpbir2an	$⊢ \emptyset : \emptyset \underset{1-1 onto}{⟶} \emptyset$