Theorem 0fin

Description: The empty set is finite. (Contributed by FL, 14-Jul-2008)

	Ref	Expression
Assertion	0fin	⊢ ∅ ∈ Fin

Proof

Step	Hyp	Ref	Expression
1		peano1	⊢ ∅ ∈ ω
2		ssid	⊢ ∅ ⊆ ∅
3		ssnnfi	⊢ ( ( ∅ ∈ ω ∧ ∅ ⊆ ∅ ) → ∅ ∈ Fin )
4	1 2 3	mp2an	⊢ ∅ ∈ Fin