Detailed syntax breakdown of Definition df-rngiso
Step | Hyp | Ref
| Expression |
1 | | crs 19945 |
. 2
class
RingIso |
2 | | vr |
. . 3
setvar 𝑟 |
3 | | vs |
. . 3
setvar 𝑠 |
4 | | cvv 3430 |
. . 3
class
V |
5 | | vf |
. . . . . . 7
setvar 𝑓 |
6 | 5 | cv 1538 |
. . . . . 6
class 𝑓 |
7 | 6 | ccnv 5584 |
. . . . 5
class ◡𝑓 |
8 | 3 | cv 1538 |
. . . . . 6
class 𝑠 |
9 | 2 | cv 1538 |
. . . . . 6
class 𝑟 |
10 | | crh 19944 |
. . . . . 6
class
RingHom |
11 | 8, 9, 10 | co 7268 |
. . . . 5
class (𝑠 RingHom 𝑟) |
12 | 7, 11 | wcel 2106 |
. . . 4
wff ◡𝑓 ∈ (𝑠 RingHom 𝑟) |
13 | 9, 8, 10 | co 7268 |
. . . 4
class (𝑟 RingHom 𝑠) |
14 | 12, 5, 13 | crab 3068 |
. . 3
class {𝑓 ∈ (𝑟 RingHom 𝑠) ∣ ◡𝑓 ∈ (𝑠 RingHom 𝑟)} |
15 | 2, 3, 4, 4, 14 | cmpo 7270 |
. 2
class (𝑟 ∈ V, 𝑠 ∈ V ↦ {𝑓 ∈ (𝑟 RingHom 𝑠) ∣ ◡𝑓 ∈ (𝑠 RingHom 𝑟)}) |
16 | 1, 15 | wceq 1539 |
1
wff RingIso =
(𝑟 ∈ V, 𝑠 ∈ V ↦ {𝑓 ∈ (𝑟 RingHom 𝑠) ∣ ◡𝑓 ∈ (𝑠 RingHom 𝑟)}) |