Definition df-made 33286

Description: Define the made by function. This function carries an ordinal to all surreals made by sections of surreals older than it. (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 33281	. 2 class M
2		vf	. . . 4 setvar 𝑓
3		cvv 3496	. . . 4 class V
4		cscut 33254	. . . . 5 class |s
5	2	cv 1536	. . . . . . . . 9 class 𝑓
6	5	crn 5558	. . . . . . . 8 class ran 𝑓
7	6	cuni 4840	. . . . . . 7 class ∪ ran 𝑓
8	7	cpw 4541	. . . . . 6 class 𝒫 ∪ ran 𝑓
9	8, 8	cxp 5555	. . . . 5 class (𝒫 ∪ ran 𝑓 × 𝒫 ∪ ran 𝑓)
10	4, 9	cima 5560	. . . 4 class ( |s “ (𝒫 ∪ ran 𝑓 × 𝒫 ∪ ran 𝑓))
11	2, 3, 10	cmpt 5148	. . 3 class (𝑓 ∈ V ↦ ( |s “ (𝒫 ∪ ran 𝑓 × 𝒫 ∪ ran 𝑓)))
12	11	crecs 8009	. 2 class recs((𝑓 ∈ V ↦ ( |s “ (𝒫 ∪ ran 𝑓 × 𝒫 ∪ ran 𝑓))))
13	1, 12	wceq 1537	1 wff M = recs((𝑓 ∈ V ↦ ( |s “ (𝒫 ∪ ran 𝑓 × 𝒫 ∪ ran 𝑓))))

This definition is referenced by:  madeval  33291