Metamath Proof Explorer


Theorem leftnod

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

Ref Expression
Hypothesis leftel.1
|- ( ph -> A e. ( _Left ` B ) )
Assertion leftnod
|- ( ph -> A e. No )

Proof

Step Hyp Ref Expression
1 leftel.1
 |-  ( ph -> A e. ( _Left ` B ) )
2 leftno
 |-  ( A e. ( _Left ` B ) -> A e. No )
3 1 2 syl
 |-  ( ph -> A e. No )