Detailed syntax breakdown of Definition df-sbg
| Step | Hyp | Ref
| Expression |
| 1 | | csg 18953 |
. 2
class
-g |
| 2 | | vg |
. . 3
setvar 𝑔 |
| 3 | | cvv 3480 |
. . 3
class
V |
| 4 | | vx |
. . . 4
setvar 𝑥 |
| 5 | | vy |
. . . 4
setvar 𝑦 |
| 6 | 2 | cv 1539 |
. . . . 5
class 𝑔 |
| 7 | | cbs 17247 |
. . . . 5
class
Base |
| 8 | 6, 7 | cfv 6561 |
. . . 4
class
(Base‘𝑔) |
| 9 | 4 | cv 1539 |
. . . . 5
class 𝑥 |
| 10 | 5 | cv 1539 |
. . . . . 6
class 𝑦 |
| 11 | | cminusg 18952 |
. . . . . . 7
class
invg |
| 12 | 6, 11 | cfv 6561 |
. . . . . 6
class
(invg‘𝑔) |
| 13 | 10, 12 | cfv 6561 |
. . . . 5
class
((invg‘𝑔)‘𝑦) |
| 14 | | cplusg 17297 |
. . . . . 6
class
+g |
| 15 | 6, 14 | cfv 6561 |
. . . . 5
class
(+g‘𝑔) |
| 16 | 9, 13, 15 | co 7431 |
. . . 4
class (𝑥(+g‘𝑔)((invg‘𝑔)‘𝑦)) |
| 17 | 4, 5, 8, 8, 16 | cmpo 7433 |
. . 3
class (𝑥 ∈ (Base‘𝑔), 𝑦 ∈ (Base‘𝑔) ↦ (𝑥(+g‘𝑔)((invg‘𝑔)‘𝑦))) |
| 18 | 2, 3, 17 | cmpt 5225 |
. 2
class (𝑔 ∈ V ↦ (𝑥 ∈ (Base‘𝑔), 𝑦 ∈ (Base‘𝑔) ↦ (𝑥(+g‘𝑔)((invg‘𝑔)‘𝑦)))) |
| 19 | 1, 18 | wceq 1540 |
1
wff
-g = (𝑔
∈ V ↦ (𝑥 ∈
(Base‘𝑔), 𝑦 ∈ (Base‘𝑔) ↦ (𝑥(+g‘𝑔)((invg‘𝑔)‘𝑦)))) |