Metamath Proof Explorer

Theorem oldno

Description: An element of an old set is a surreal. (Contributed by Scott Fenton, 27-Feb-2026)

Ref Expression
Assertion oldno 
|- ( A e. ( _Old ` B ) -> A e. No )

Proof

Step Hyp Ref Expression
1 oldssno 
 |-  ( _Old ` B ) C_ No
2 1 sseli 
 |-  ( A e. ( _Old ` B ) -> A e. No )