Detailed syntax breakdown of Definition df-uc1p
Step | Hyp | Ref
| Expression |
1 | | cuc1p 25300 |
. 2
class
Unic1p |
2 | | vr |
. . 3
setvar 𝑟 |
3 | | cvv 3433 |
. . 3
class
V |
4 | | vf |
. . . . . . 7
setvar 𝑓 |
5 | 4 | cv 1538 |
. . . . . 6
class 𝑓 |
6 | 2 | cv 1538 |
. . . . . . . 8
class 𝑟 |
7 | | cpl1 21357 |
. . . . . . . 8
class
Poly1 |
8 | 6, 7 | cfv 6437 |
. . . . . . 7
class
(Poly1‘𝑟) |
9 | | c0g 17159 |
. . . . . . 7
class
0g |
10 | 8, 9 | cfv 6437 |
. . . . . 6
class
(0g‘(Poly1‘𝑟)) |
11 | 5, 10 | wne 2944 |
. . . . 5
wff 𝑓 ≠
(0g‘(Poly1‘𝑟)) |
12 | | cdg1 25225 |
. . . . . . . . 9
class
deg1 |
13 | 6, 12 | cfv 6437 |
. . . . . . . 8
class (
deg1 ‘𝑟) |
14 | 5, 13 | cfv 6437 |
. . . . . . 7
class ((
deg1 ‘𝑟)‘𝑓) |
15 | | cco1 21358 |
. . . . . . . 8
class
coe1 |
16 | 5, 15 | cfv 6437 |
. . . . . . 7
class
(coe1‘𝑓) |
17 | 14, 16 | cfv 6437 |
. . . . . 6
class
((coe1‘𝑓)‘(( deg1 ‘𝑟)‘𝑓)) |
18 | | cui 19890 |
. . . . . . 7
class
Unit |
19 | 6, 18 | cfv 6437 |
. . . . . 6
class
(Unit‘𝑟) |
20 | 17, 19 | wcel 2107 |
. . . . 5
wff
((coe1‘𝑓)‘(( deg1 ‘𝑟)‘𝑓)) ∈ (Unit‘𝑟) |
21 | 11, 20 | wa 396 |
. . . 4
wff (𝑓 ≠
(0g‘(Poly1‘𝑟)) ∧ ((coe1‘𝑓)‘(( deg1
‘𝑟)‘𝑓)) ∈ (Unit‘𝑟)) |
22 | | cbs 16921 |
. . . . 5
class
Base |
23 | 8, 22 | cfv 6437 |
. . . 4
class
(Base‘(Poly1‘𝑟)) |
24 | 21, 4, 23 | crab 3069 |
. . 3
class {𝑓 ∈
(Base‘(Poly1‘𝑟)) ∣ (𝑓 ≠
(0g‘(Poly1‘𝑟)) ∧ ((coe1‘𝑓)‘(( deg1
‘𝑟)‘𝑓)) ∈ (Unit‘𝑟))} |
25 | 2, 3, 24 | cmpt 5158 |
. 2
class (𝑟 ∈ V ↦ {𝑓 ∈
(Base‘(Poly1‘𝑟)) ∣ (𝑓 ≠
(0g‘(Poly1‘𝑟)) ∧ ((coe1‘𝑓)‘(( deg1
‘𝑟)‘𝑓)) ∈ (Unit‘𝑟))}) |
26 | 1, 25 | wceq 1539 |
1
wff
Unic1p = (𝑟 ∈ V ↦ {𝑓 ∈
(Base‘(Poly1‘𝑟)) ∣ (𝑓 ≠
(0g‘(Poly1‘𝑟)) ∧ ((coe1‘𝑓)‘(( deg1
‘𝑟)‘𝑓)) ∈ (Unit‘𝑟))}) |