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 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 5937 . 2 class +𝑜
2 vx . . 3 setvar x
3 vy . . 3 setvar y
4 con0 4066 . . 3 class On
53cv 1241 . . . 4 class y
6 vz . . . . . 6 setvar z
7 cvv 2551 . . . . . 6 class V
86cv 1241 . . . . . . 7 class z
98csuc 4068 . . . . . 6 class suc z
106, 7, 9cmpt 3809 . . . . 5 class (z V ↦ suc z)
112cv 1241 . . . . 5 class x
1210, 11crdg 5896 . . . 4 class rec((z V ↦ suc z), x)
135, 12cfv 4845 . . 3 class (rec((z V ↦ suc z), x)‘y)
142, 3, 4, 4, 13cmpt2 5457 . 2 class (x On, y On ↦ (rec((z V ↦ suc z), x)‘y))
151, 14wceq 1242 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  5966  oaexg  5967  oav  5973
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