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Definition df-oadd 5916
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
StepHypRef Expression
1 coa 5909 . 2 class +𝑜
2 vx . . 3 setvar x
3 vy . . 3 setvar y
4 con0 4045 . . 3 class On
53cv 1225 . . . 4 class y
6 vz . . . . . 6 setvar z
7 cvv 2531 . . . . . 6 class V
86cv 1225 . . . . . . 7 class z
98csuc 4047 . . . . . 6 class suc z
106, 7, 9cmpt 3788 . . . . 5 class (z V ↦ suc z)
112cv 1225 . . . . 5 class x
1210, 11crdg 5873 . . . 4 class rec((z V ↦ suc z), x)
135, 12cfv 4825 . . 3 class (rec((z V ↦ suc z), x)‘y)
142, 3, 4, 4, 13cmpt2 5434 . 2 class (x On, y On ↦ (rec((z V ↦ suc z), x)‘y))
151, 14wceq 1226 1 wff +𝑜 = (x On, y On ↦ (rec((z V ↦ suc z), x)‘y))
Colors of variables: wff set class
This definition is referenced by:  fnoa  5938  oaexg  5939  oav  5945
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