Detailed syntax breakdown of Definition df-wspthsn
Step | Hyp | Ref
| Expression |
1 | | cwwspthsn 27912 |
. 2
class
WSPathsN |
2 | | vn |
. . 3
setvar 𝑛 |
3 | | vg |
. . 3
setvar 𝑔 |
4 | | cn0 12090 |
. . 3
class
ℕ0 |
5 | | cvv 3408 |
. . 3
class
V |
6 | | vf |
. . . . . . 7
setvar 𝑓 |
7 | 6 | cv 1542 |
. . . . . 6
class 𝑓 |
8 | | vw |
. . . . . . 7
setvar 𝑤 |
9 | 8 | cv 1542 |
. . . . . 6
class 𝑤 |
10 | 3 | cv 1542 |
. . . . . . 7
class 𝑔 |
11 | | cspths 27800 |
. . . . . . 7
class
SPaths |
12 | 10, 11 | cfv 6380 |
. . . . . 6
class
(SPaths‘𝑔) |
13 | 7, 9, 12 | wbr 5053 |
. . . . 5
wff 𝑓(SPaths‘𝑔)𝑤 |
14 | 13, 6 | wex 1787 |
. . . 4
wff
∃𝑓 𝑓(SPaths‘𝑔)𝑤 |
15 | 2 | cv 1542 |
. . . . 5
class 𝑛 |
16 | | cwwlksn 27910 |
. . . . 5
class
WWalksN |
17 | 15, 10, 16 | co 7213 |
. . . 4
class (𝑛 WWalksN 𝑔) |
18 | 14, 8, 17 | crab 3065 |
. . 3
class {𝑤 ∈ (𝑛 WWalksN 𝑔) ∣ ∃𝑓 𝑓(SPaths‘𝑔)𝑤} |
19 | 2, 3, 4, 5, 18 | cmpo 7215 |
. 2
class (𝑛 ∈ ℕ0,
𝑔 ∈ V ↦ {𝑤 ∈ (𝑛 WWalksN 𝑔) ∣ ∃𝑓 𝑓(SPaths‘𝑔)𝑤}) |
20 | 1, 19 | wceq 1543 |
1
wff WSPathsN =
(𝑛 ∈
ℕ0, 𝑔
∈ V ↦ {𝑤 ∈
(𝑛 WWalksN 𝑔) ∣ ∃𝑓 𝑓(SPaths‘𝑔)𝑤}) |