Metamath Proof Explorer

Theorem addsid1d

Description: Surreal addition to zero is identity. Part of Theorem 3 of Conway p. 17. (Contributed by Scott Fenton, 20-Aug-2024)

Ref Expression
Hypothesis addsid1d.1 
|- ( ph -> A e. No )
Assertion addsid1d 
|- ( ph -> ( A +s 0s ) = A )

Proof

Step Hyp Ref Expression
1 addsid1d.1 
 |-  ( ph -> A e. No )
2 addsid1 
 |-  ( A e. No -> ( A +s 0s ) = A )
3 1 2 syl 
 |-  ( ph -> ( A +s 0s ) = A )