Detailed syntax breakdown of Definition df-lsatoms
| Step | Hyp | Ref
| Expression |
| 1 | | clsa 38975 |
. 2
class
LSAtoms |
| 2 | | vw |
. . 3
setvar 𝑤 |
| 3 | | cvv 3480 |
. . 3
class
V |
| 4 | | vv |
. . . . 5
setvar 𝑣 |
| 5 | 2 | cv 1539 |
. . . . . . 7
class 𝑤 |
| 6 | | cbs 17247 |
. . . . . . 7
class
Base |
| 7 | 5, 6 | cfv 6561 |
. . . . . 6
class
(Base‘𝑤) |
| 8 | | c0g 17484 |
. . . . . . . 8
class
0g |
| 9 | 5, 8 | cfv 6561 |
. . . . . . 7
class
(0g‘𝑤) |
| 10 | 9 | csn 4626 |
. . . . . 6
class
{(0g‘𝑤)} |
| 11 | 7, 10 | cdif 3948 |
. . . . 5
class
((Base‘𝑤)
∖ {(0g‘𝑤)}) |
| 12 | 4 | cv 1539 |
. . . . . . 7
class 𝑣 |
| 13 | 12 | csn 4626 |
. . . . . 6
class {𝑣} |
| 14 | | clspn 20969 |
. . . . . . 7
class
LSpan |
| 15 | 5, 14 | cfv 6561 |
. . . . . 6
class
(LSpan‘𝑤) |
| 16 | 13, 15 | cfv 6561 |
. . . . 5
class
((LSpan‘𝑤)‘{𝑣}) |
| 17 | 4, 11, 16 | cmpt 5225 |
. . . 4
class (𝑣 ∈ ((Base‘𝑤) ∖
{(0g‘𝑤)})
↦ ((LSpan‘𝑤)‘{𝑣})) |
| 18 | 17 | crn 5686 |
. . 3
class ran
(𝑣 ∈
((Base‘𝑤) ∖
{(0g‘𝑤)})
↦ ((LSpan‘𝑤)‘{𝑣})) |
| 19 | 2, 3, 18 | cmpt 5225 |
. 2
class (𝑤 ∈ V ↦ ran (𝑣 ∈ ((Base‘𝑤) ∖
{(0g‘𝑤)})
↦ ((LSpan‘𝑤)‘{𝑣}))) |
| 20 | 1, 19 | wceq 1540 |
1
wff LSAtoms =
(𝑤 ∈ V ↦ ran
(𝑣 ∈
((Base‘𝑤) ∖
{(0g‘𝑤)})
↦ ((LSpan‘𝑤)‘{𝑣}))) |