Detailed syntax breakdown of Definition df-oadd
Step | Hyp | Ref
| Expression |
1 | | coa 7444 |
. 2
class
+𝑜 |
2 | | vx |
. . 3
setvar 𝑥 |
3 | | vy |
. . 3
setvar 𝑦 |
4 | | con0 5640 |
. . 3
class
On |
5 | 3 | cv 1474 |
. . . 4
class 𝑦 |
6 | | vz |
. . . . . 6
setvar 𝑧 |
7 | | cvv 3173 |
. . . . . 6
class
V |
8 | 6 | cv 1474 |
. . . . . . 7
class 𝑧 |
9 | 8 | csuc 5642 |
. . . . . 6
class suc 𝑧 |
10 | 6, 7, 9 | cmpt 4643 |
. . . . 5
class (𝑧 ∈ V ↦ suc 𝑧) |
11 | 2 | cv 1474 |
. . . . 5
class 𝑥 |
12 | 10, 11 | crdg 7392 |
. . . 4
class
rec((𝑧 ∈ V
↦ suc 𝑧), 𝑥) |
13 | 5, 12 | cfv 5804 |
. . 3
class
(rec((𝑧 ∈ V
↦ suc 𝑧), 𝑥)‘𝑦) |
14 | 2, 3, 4, 4, 13 | cmpt2 6551 |
. 2
class (𝑥 ∈ On, 𝑦 ∈ On ↦ (rec((𝑧 ∈ V ↦ suc 𝑧), 𝑥)‘𝑦)) |
15 | 1, 14 | wceq 1475 |
1
wff
+𝑜 = (𝑥
∈ On, 𝑦 ∈ On
↦ (rec((𝑧 ∈ V
↦ suc 𝑧), 𝑥)‘𝑦)) |