Metamath Proof Explorer


Definition df-new

Description: Define the newer than function. This function carries an ordinal to all surreals made on that day. Definition from Conway p. 29. (Contributed by Scott Fenton, 17-Dec-2021)

Ref Expression
Assertion df-new Could not format assertion : No typesetting found for |- _New = ( x e. On |-> ( ( _Made ` x ) \ ( _Old ` x ) ) ) with typecode |-

Detailed syntax breakdown

Step Hyp Ref Expression
0 cnew Could not format _New : No typesetting found for class _New with typecode class
1 vx setvarx
2 con0 classOn
3 cmade Could not format _Made : No typesetting found for class _Made with typecode class
4 1 cv setvarx
5 4 3 cfv Could not format ( _Made ` x ) : No typesetting found for class ( _Made ` x ) with typecode class
6 cold classOld
7 4 6 cfv classOldx
8 5 7 cdif Could not format ( ( _Made ` x ) \ ( _Old ` x ) ) : No typesetting found for class ( ( _Made ` x ) \ ( _Old ` x ) ) with typecode class
9 1 2 8 cmpt Could not format ( x e. On |-> ( ( _Made ` x ) \ ( _Old ` x ) ) ) : No typesetting found for class ( x e. On |-> ( ( _Made ` x ) \ ( _Old ` x ) ) ) with typecode class
10 0 9 wceq Could not format _New = ( x e. On |-> ( ( _Made ` x ) \ ( _Old ` x ) ) ) : No typesetting found for wff _New = ( x e. On |-> ( ( _Made ` x ) \ ( _Old ` x ) ) ) with typecode wff