Definition df-oadd 6572

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

Assertion

Ref	Expression
df-oadd	|- +o = ( x e. On , y e. On |-> ( rec ( ( z e. _V |-> suc z ) , x ) ` y ) )

Distinct variable group:   x, y, z

Detailed syntax breakdown of Definition df-oadd

Step	Hyp	Ref	Expression
1		coa 6565	. 2 class +o
2		vx	. . 3 setvar x
3		vy	. . 3 setvar y
4		con0 4454	. . 3 class On
5	3	cv 1394	. . . 4 class y
6		vz	. . . . . 6 setvar z
7		cvv 2799	. . . . . 6 class _V
8	6	cv 1394	. . . . . . 7 class z
9	8	csuc 4456	. . . . . 6 class suc z
10	6, 7, 9	cmpt 4145	. . . . 5 class ( z e. _V |-> suc z )
11	2	cv 1394	. . . . 5 class x
12	10, 11	crdg 6521	. . . 4 class rec ( ( z e. _V |-> suc z ) , x )
13	5, 12	cfv 5318	. . 3 class ( rec ( ( z e. _V |-> suc z ) , x ) ` y )
14	2, 3, 4, 4, 13	cmpo 6009	. 2 class ( x e. On , y e. On |-> ( rec ( ( z e. _V |-> suc z ) , x ) ` y ) )
15	1, 14	wceq 1395	1 wff +o = ( x e. On , y e. On |-> ( rec ( ( z e. _V |-> suc z ) , x ) ` y ) )

This definition is referenced by:  fnoa  6601  oaexg  6602  oav  6608