Definition df-new 31932

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

Assertion

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

Detailed syntax breakdown of Definition df-new

Step	Hyp	Ref	Expression
1		cnew 31927	. 2 class N
2		vx	. . 3 setvar 𝑥
3		con0 5723	. . 3 class On
4	2	cv 1482	. . . . 5 class 𝑥
5		cold 31926	. . . . 5 class O
6	4, 5	cfv 5888	. . . 4 class ( O ‘𝑥)
7		cmade 31925	. . . . 5 class M
8	4, 7	cfv 5888	. . . 4 class ( M ‘𝑥)
9	6, 8	cdif 3571	. . 3 class (( O ‘𝑥) ∖ ( M ‘𝑥))
10	2, 3, 9	cmpt 4729	. 2 class (𝑥 ∈ On ↦ (( O ‘𝑥) ∖ ( M ‘𝑥)))
11	1, 10	wceq 1483	1 wff N = (𝑥 ∈ On ↦ (( O ‘𝑥) ∖ ( M ‘𝑥)))

This definition is referenced by: (None)