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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	⊢ ∅ : ∅ –1-1-onto→ ∅

Step	Hyp	Ref	Expression
1		eqid	⊢ ∅ = ∅
2		f1o00	⊢ ( ∅ : ∅ –1-1-onto→ ∅ ↔ ( ∅ = ∅ ∧ ∅ = ∅ ) )
3	1 1 2	mpbir2an	⊢ ∅ : ∅ –1-1-onto→ ∅