Metamath Proof Explorer


Definition df-2s

Description: Define surreal two. This is the simplest number greater than one. See 1p1e2s for its addition version. (Contributed by Scott Fenton, 27-May-2025)

Ref Expression
Assertion df-2s
|- 2s = ( { 1s } |s (/) )

Detailed syntax breakdown

Step Hyp Ref Expression
0 c2s
 |-  2s
1 c1s
 |-  1s
2 1 csn
 |-  { 1s }
3 cscut
 |-  |s
4 c0
 |-  (/)
5 2 4 3 co
 |-  ( { 1s } |s (/) )
6 0 5 wceq
 |-  2s = ( { 1s } |s (/) )