Metamath Proof Explorer

Theorem newnod

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

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

Proof

Step Hyp Ref Expression
1 newnod.1 
 |-  ( ph -> A e. ( _New ` B ) )
2 newssno 
 |-  ( _New ` B ) C_ No
3 2 1 sselid 
 |-  ( ph -> A e. No )