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Definition df-oadd 6139
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 6132 . 2 class +𝑜
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 con0 4164 . . 3 class On
53cv 1286 . . . 4 class 𝑦
6 vz . . . . . 6 setvar 𝑧
7 cvv 2615 . . . . . 6 class V
86cv 1286 . . . . . . 7 class 𝑧
98csuc 4166 . . . . . 6 class suc 𝑧
106, 7, 9cmpt 3874 . . . . 5 class (𝑧 ∈ V ↦ suc 𝑧)
112cv 1286 . . . . 5 class 𝑥
1210, 11crdg 6088 . . . 4 class rec((𝑧 ∈ V ↦ suc 𝑧), 𝑥)
135, 12cfv 4981 . . 3 class (rec((𝑧 ∈ V ↦ suc 𝑧), 𝑥)‘𝑦)
142, 3, 4, 4, 13cmpt2 5615 . 2 class (𝑥 ∈ On, 𝑦 ∈ On ↦ (rec((𝑧 ∈ V ↦ suc 𝑧), 𝑥)‘𝑦))
151, 14wceq 1287 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  6162  oaexg  6163  oav  6169
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