Definition df-oadd 5944

Description: Define the ordinal addition operation. (Contributed by NM, 3-May-1995.)

Assertion

Ref	Expression
df-oadd	⊢ +𝑜 = (x ∈ On, y ∈ On ↦ (rec((z ∈ V ↦ suc z), x)‘y))

Distinct variable group:   x,y,z

Detailed syntax breakdown of Definition df-oadd

Step	Hyp	Ref	Expression
1		coa 5937	. 2 class +𝑜
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		con0 4066	. . 3 class On
5	3	cv 1241	. . . 4 class y
6		vz	. . . . . 6 setvar z
7		cvv 2551	. . . . . 6 class V
8	6	cv 1241	. . . . . . 7 class z
9	8	csuc 4068	. . . . . 6 class suc z
10	6, 7, 9	cmpt 3809	. . . . 5 class (z ∈ V ↦ suc z)
11	2	cv 1241	. . . . 5 class x
12	10, 11	crdg 5896	. . . 4 class rec((z ∈ V ↦ suc z), x)
13	5, 12	cfv 4845	. . 3 class (rec((z ∈ V ↦ suc z), x)‘y)
14	2, 3, 4, 4, 13	cmpt2 5457	. 2 class (x ∈ On, y ∈ On ↦ (rec((z ∈ V ↦ suc z), x)‘y))
15	1, 14	wceq 1242	1 wff +𝑜 = (x ∈ On, y ∈ On ↦ (rec((z ∈ V ↦ suc z), x)‘y))

This definition is referenced by:  fnoa  5966  oaexg  5967  oav  5973