Metamath Proof Explorer

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