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Definition df-oadd 7803
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 7796 . 2 class +𝑜
2 vx . . 3 setvar 𝑥
3 vy . . 3 setvar 𝑦
4 con0 5943 . . 3 class On
53cv 1636 . . . 4 class 𝑦
6 vz . . . . . 6 setvar 𝑧
7 cvv 3398 . . . . . 6 class V
86cv 1636 . . . . . . 7 class 𝑧
98csuc 5945 . . . . . 6 class suc 𝑧
106, 7, 9cmpt 4930 . . . . 5 class (𝑧 ∈ V ↦ suc 𝑧)
112cv 1636 . . . . 5 class 𝑥
1210, 11crdg 7744 . . . 4 class rec((𝑧 ∈ V ↦ suc 𝑧), 𝑥)
135, 12cfv 6104 . . 3 class (rec((𝑧 ∈ V ↦ suc 𝑧), 𝑥)‘𝑦)
142, 3, 4, 4, 13cmpt2 6879 . 2 class (𝑥 ∈ On, 𝑦 ∈ On ↦ (rec((𝑧 ∈ V ↦ suc 𝑧), 𝑥)‘𝑦))
151, 14wceq 1637 1 wff +𝑜 = (𝑥 ∈ On, 𝑦 ∈ On ↦ (rec((𝑧 ∈ V ↦ suc 𝑧), 𝑥)‘𝑦))
Colors of variables: wff setvar class
This definition is referenced by:  fnoa  7828  oav  7831
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