Definition df-negs 28407

Description: Define surreal negation. Definition from [Conway] p. 5. (Contributed by Scott Fenton, 20-Aug-2024.)

Assertion

Ref	Expression
df-negs	⊢ -s = norec ((𝑥 ∈ V, 𝑛 ∈ V ↦ ((𝑛 “ (R‘𝑥)) |s (𝑛 “ (L‘𝑥)))))

Distinct variable group:   𝑥,𝑛

Detailed syntax breakdown of Definition df-negs

Step	Hyp	Ref	Expression
1		cnegs 28405	. 2 class -s
2		vx	. . . 4 setvar 𝑥
3		vn	. . . 4 setvar 𝑛
4		cvv 3451	. . . 4 class V
5	3	cv 1569	. . . . . 6 class 𝑛
6	2	cv 1569	. . . . . . 7 class 𝑥
7		cright 28212	. . . . . . 7 class R
8	6, 7	cfv 6538	. . . . . 6 class (R‘𝑥)
9	5, 8	cima 5654	. . . . 5 class (𝑛 “ (R‘𝑥))
10		cleft 28211	. . . . . . 7 class L
11	6, 10	cfv 6538	. . . . . 6 class (L‘𝑥)
12	5, 11	cima 5654	. . . . 5 class (𝑛 “ (L‘𝑥))
13		ccuts 28145	. . . . 5 class |s
14	9, 12, 13	co 7420	. . . 4 class ((𝑛 “ (R‘𝑥)) |s (𝑛 “ (L‘𝑥)))
15	2, 3, 4, 4, 14	cmpo 7422	. . 3 class (𝑥 ∈ V, 𝑛 ∈ V ↦ ((𝑛 “ (R‘𝑥)) |s (𝑛 “ (L‘𝑥))))
16	15	cnorec 28323	. 2 class norec ((𝑥 ∈ V, 𝑛 ∈ V ↦ ((𝑛 “ (R‘𝑥)) |s (𝑛 “ (L‘𝑥)))))
17	1, 16	wceq 1570	1 wff -s = norec ((𝑥 ∈ V, 𝑛 ∈ V ↦ ((𝑛 “ (R‘𝑥)) |s (𝑛 “ (L‘𝑥)))))

This definition is used by:  negsfn  28409  negsval  28411