Detailed syntax breakdown of Definition df-wspthsn
Step | Hyp | Ref
| Expression |
1 | | cwwspthsn 41031 |
. 2
class
WSPathsN |
2 | | vn |
. . 3
setvar 𝑛 |
3 | | vg |
. . 3
setvar 𝑔 |
4 | | cn0 11169 |
. . 3
class
ℕ0 |
5 | | cvv 3173 |
. . 3
class
V |
6 | | vf |
. . . . . . 7
setvar 𝑓 |
7 | 6 | cv 1474 |
. . . . . 6
class 𝑓 |
8 | | vw |
. . . . . . 7
setvar 𝑤 |
9 | 8 | cv 1474 |
. . . . . 6
class 𝑤 |
10 | 3 | cv 1474 |
. . . . . . 7
class 𝑔 |
11 | | cspths 40920 |
. . . . . . 7
class
SPathS |
12 | 10, 11 | cfv 5804 |
. . . . . 6
class
(SPathS‘𝑔) |
13 | 7, 9, 12 | wbr 4583 |
. . . . 5
wff 𝑓(SPathS‘𝑔)𝑤 |
14 | 13, 6 | wex 1695 |
. . . 4
wff
∃𝑓 𝑓(SPathS‘𝑔)𝑤 |
15 | 2 | cv 1474 |
. . . . 5
class 𝑛 |
16 | | cwwlksn 41029 |
. . . . 5
class
WWalkSN |
17 | 15, 10, 16 | co 6549 |
. . . 4
class (𝑛 WWalkSN 𝑔) |
18 | 14, 8, 17 | crab 2900 |
. . 3
class {𝑤 ∈ (𝑛 WWalkSN 𝑔) ∣ ∃𝑓 𝑓(SPathS‘𝑔)𝑤} |
19 | 2, 3, 4, 5, 18 | cmpt2 6551 |
. 2
class (𝑛 ∈ ℕ0,
𝑔 ∈ V ↦ {𝑤 ∈ (𝑛 WWalkSN 𝑔) ∣ ∃𝑓 𝑓(SPathS‘𝑔)𝑤}) |
20 | 1, 19 | wceq 1475 |
1
wff WSPathsN =
(𝑛 ∈
ℕ0, 𝑔
∈ V ↦ {𝑤 ∈
(𝑛 WWalkSN 𝑔) ∣ ∃𝑓 𝑓(SPathS‘𝑔)𝑤}) |