Definition df-new 28224

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 28219	. 2 class N
2		vx	. . 3 setvar 𝑥
3		con0 6365	. . 3 class On
4	2	cv 1568	. . . . 5 class 𝑥
5		cmade 28217	. . . . 5 class M
6	4, 5	cfv 6543	. . . 4 class (M‘𝑥)
7		cold 28218	. . . . 5 class O
8	4, 7	cfv 6543	. . . 4 class (O‘𝑥)
9	6, 8	cdif 4044	. . 3 class ((M‘𝑥) ∖ (O‘𝑥))
10	2, 3, 9	cmpt 5185	. 2 class (𝑥 ∈ On ↦ ((M‘𝑥) ∖ (O‘𝑥)))
11	1, 10	wceq 1569	1 wff N = (𝑥 ∈ On ↦ ((M‘𝑥) ∖ (O‘𝑥)))

This definition is used by:  newval  28230  newf  28233