Metamath Proof Explorer

Theorem 0no

Description: Ordinal zero maps to a surreal number. (Contributed by RP, 21-Sep-2023)

Ref Expression
Assertion 0no 
|- (/) e. No

Proof

Step Hyp Ref Expression
1 0xp 
 |-  ( (/) X. { 2o } ) = (/)
2 0elon 
 |-  (/) e. On
3 2 onnoi 
 |-  ( (/) X. { 2o } ) e. No
4 1 3 eqeltrri 
 |-  (/) e. No