Metamath Proof Explorer


Theorem 1finon

Description: 1 is a finite ordinal. See 1onn . (Contributed by RP, 27-Sep-2023)

Ref Expression
Assertion 1finon 1o ∈ ( On ∩ Fin )

Proof

Step Hyp Ref Expression
1 1onn ⊢ 1o ∈ ω
2 onfin2 ⊢ ω = ( On ∩ Fin )
3 1 2 eleqtri ⊢ 1o ∈ ( On ∩ Fin )