Definition df-made 34031

Description: Define the made by function. This function carries an ordinal to all surreals made by sections of surreals older than it. Definition from [Conway] p. 29. (Contributed by Scott Fenton, 17-Dec-2021.)

Assertion

Ref	Expression
df-made	⊢ M = recs((𝑓 ∈ V ↦ ( |s “ (𝒫 ∪ ran 𝑓 × 𝒫 ∪ ran 𝑓))))

Detailed syntax breakdown of Definition df-made

Step	Hyp	Ref	Expression
1		cmade 34026	. 2 class M
2		vf	. . . 4 setvar 𝑓
3		cvv 3432	. . . 4 class V
4		cscut 33977	. . . . 5 class |s
5	2	cv 1538	. . . . . . . . 9 class 𝑓
6	5	crn 5590	. . . . . . . 8 class ran 𝑓
7	6	cuni 4839	. . . . . . 7 class ∪ ran 𝑓
8	7	cpw 4533	. . . . . 6 class 𝒫 ∪ ran 𝑓
9	8, 8	cxp 5587	. . . . 5 class (𝒫 ∪ ran 𝑓 × 𝒫 ∪ ran 𝑓)
10	4, 9	cima 5592	. . . 4 class ( |s “ (𝒫 ∪ ran 𝑓 × 𝒫 ∪ ran 𝑓))
11	2, 3, 10	cmpt 5157	. . 3 class (𝑓 ∈ V ↦ ( |s “ (𝒫 ∪ ran 𝑓 × 𝒫 ∪ ran 𝑓)))
12	11	crecs 8201	. 2 class recs((𝑓 ∈ V ↦ ( |s “ (𝒫 ∪ ran 𝑓 × 𝒫 ∪ ran 𝑓))))
13	1, 12	wceq 1539	1 wff M = recs((𝑓 ∈ V ↦ ( |s “ (𝒫 ∪ ran 𝑓 × 𝒫 ∪ ran 𝑓))))

This definition is referenced by:  madeval  34036  oldval  34038  newval  34039  madef  34040