Metamath Proof Explorer

Theorem elnn

Description: A member of a natural number is a natural number. (Contributed by NM, 21-Jun-1998)

Ref Expression
Assertion elnn 
|- ( ( A e. B /\ B e. _om ) -> A e. _om )

Proof

Step Hyp Ref Expression
1 ordom 
 |-  Ord _om
2 ordtr 
 |-  ( Ord _om -> Tr _om )
3 trel 
 |-  ( Tr _om -> ( ( A e. B /\ B e. _om ) -> A e. _om ) )
4 1 2 3 mp2b 
 |-  ( ( A e. B /\ B e. _om ) -> A e. _om )