Definition df-new 34033

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.)

Assertion

Ref	Expression
df-new	⊢ N = (𝑥 ∈ On ↦ (( M ‘𝑥) ∖ ( O ‘𝑥)))

Detailed syntax breakdown of Definition df-new

Step	Hyp	Ref	Expression
1		cnew 34028	. 2 class N
2		vx	. . 3 setvar 𝑥
3		con0 6266	. . 3 class On
4	2	cv 1538	. . . . 5 class 𝑥
5		cmade 34026	. . . . 5 class M
6	4, 5	cfv 6433	. . . 4 class ( M ‘𝑥)
7		cold 34027	. . . . 5 class O
8	4, 7	cfv 6433	. . . 4 class ( O ‘𝑥)
9	6, 8	cdif 3884	. . 3 class (( M ‘𝑥) ∖ ( O ‘𝑥))
10	2, 3, 9	cmpt 5157	. 2 class (𝑥 ∈ On ↦ (( M ‘𝑥) ∖ ( O ‘𝑥)))
11	1, 10	wceq 1539	1 wff N = (𝑥 ∈ On ↦ (( M ‘𝑥) ∖ ( O ‘𝑥)))

This definition is referenced by:  newval  34039  newf  34042