Metamath Proof Explorer

Theorem onssnel2i

Description: An ordering law for ordinal numbers. (Contributed by NM, 13-Jun-1994)

Ref Expression
Hypothesis on.1 
|- A e. On
Assertion onssnel2i 
|- ( B C_ A -> -. A e. B )

Proof

Step Hyp Ref Expression
1 on.1 
 |-  A e. On
2 1 onirri 
 |-  -. A e. A
3 ssel 
 |-  ( B C_ A -> ( A e. B -> A e. A ) )
4 2 3 mtoi 
 |-  ( B C_ A -> -. A e. B )