Metamath Proof Explorer

Theorem oldnod

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

Ref Expression
Hypothesis oldnod.1 
|- ( ph -> A e. ( _Old ` B ) )
Assertion oldnod 
|- ( ph -> A e. No )

Proof

Step Hyp Ref Expression
1 oldnod.1 
 |-  ( ph -> A e. ( _Old ` B ) )
2 oldssno 
 |-  ( _Old ` B ) C_ No
3 2 1 sselid 
 |-  ( ph -> A e. No )