Metamath Proof Explorer

Theorem nnfi

Description: Natural numbers are finite sets. (Contributed by Stefan O'Rear, 21-Mar-2015)

Ref Expression
Assertion nnfi 
|- ( A e. _om -> A e. Fin )

Proof

Step Hyp Ref Expression
1 onfin2 
 |-  _om = ( On i^i Fin )
2 inss2 
 |-  ( On i^i Fin ) C_ Fin
3 1 2 eqsstri 
 |-  _om C_ Fin
4 3 sseli 
 |-  ( A e. _om -> A e. Fin )