Metamath Proof Explorer

Theorem 0finOLD

Description: Obsolete version of 0fi as of 13-Jan-2025. (Contributed by FL, 14-Jul-2008) (Proof modification is discouraged.) (New usage is discouraged.)

Ref Expression
Assertion 0finOLD ⊢ ∅ ∈ Fin

Proof

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