Detailed syntax breakdown of Definition df-mon1
Step | Hyp | Ref
| Expression |
1 | | cmn1 25047 |
. 2
class
Monic1p |
2 | | vr |
. . 3
setvar 𝑟 |
3 | | cvv 3421 |
. . 3
class
V |
4 | | vf |
. . . . . . 7
setvar 𝑓 |
5 | 4 | cv 1542 |
. . . . . 6
class 𝑓 |
6 | 2 | cv 1542 |
. . . . . . . 8
class 𝑟 |
7 | | cpl1 21122 |
. . . . . . . 8
class
Poly1 |
8 | 6, 7 | cfv 6398 |
. . . . . . 7
class
(Poly1‘𝑟) |
9 | | c0g 16969 |
. . . . . . 7
class
0g |
10 | 8, 9 | cfv 6398 |
. . . . . 6
class
(0g‘(Poly1‘𝑟)) |
11 | 5, 10 | wne 2941 |
. . . . 5
wff 𝑓 ≠
(0g‘(Poly1‘𝑟)) |
12 | | cdg1 24973 |
. . . . . . . . 9
class
deg1 |
13 | 6, 12 | cfv 6398 |
. . . . . . . 8
class (
deg1 ‘𝑟) |
14 | 5, 13 | cfv 6398 |
. . . . . . 7
class ((
deg1 ‘𝑟)‘𝑓) |
15 | | cco1 21123 |
. . . . . . . 8
class
coe1 |
16 | 5, 15 | cfv 6398 |
. . . . . . 7
class
(coe1‘𝑓) |
17 | 14, 16 | cfv 6398 |
. . . . . 6
class
((coe1‘𝑓)‘(( deg1 ‘𝑟)‘𝑓)) |
18 | | cur 19541 |
. . . . . . 7
class
1r |
19 | 6, 18 | cfv 6398 |
. . . . . 6
class
(1r‘𝑟) |
20 | 17, 19 | wceq 1543 |
. . . . 5
wff
((coe1‘𝑓)‘(( deg1 ‘𝑟)‘𝑓)) = (1r‘𝑟) |
21 | 11, 20 | wa 399 |
. . . 4
wff (𝑓 ≠
(0g‘(Poly1‘𝑟)) ∧ ((coe1‘𝑓)‘(( deg1
‘𝑟)‘𝑓)) = (1r‘𝑟)) |
22 | | cbs 16785 |
. . . . 5
class
Base |
23 | 8, 22 | cfv 6398 |
. . . 4
class
(Base‘(Poly1‘𝑟)) |
24 | 21, 4, 23 | crab 3066 |
. . 3
class {𝑓 ∈
(Base‘(Poly1‘𝑟)) ∣ (𝑓 ≠
(0g‘(Poly1‘𝑟)) ∧ ((coe1‘𝑓)‘(( deg1
‘𝑟)‘𝑓)) = (1r‘𝑟))} |
25 | 2, 3, 24 | cmpt 5150 |
. 2
class (𝑟 ∈ V ↦ {𝑓 ∈
(Base‘(Poly1‘𝑟)) ∣ (𝑓 ≠
(0g‘(Poly1‘𝑟)) ∧ ((coe1‘𝑓)‘(( deg1
‘𝑟)‘𝑓)) = (1r‘𝑟))}) |
26 | 1, 25 | wceq 1543 |
1
wff
Monic1p = (𝑟 ∈ V ↦ {𝑓 ∈
(Base‘(Poly1‘𝑟)) ∣ (𝑓 ≠
(0g‘(Poly1‘𝑟)) ∧ ((coe1‘𝑓)‘(( deg1
‘𝑟)‘𝑓)) = (1r‘𝑟))}) |