Detailed syntax breakdown of Definition df-lat
Step | Hyp | Ref
| Expression |
1 | | clat 17045 |
. 2
class
Lat |
2 | | vp |
. . . . . . . 8
setvar 𝑝 |
3 | 2 | cv 1482 |
. . . . . . 7
class 𝑝 |
4 | | cjn 16944 |
. . . . . . 7
class
join |
5 | 3, 4 | cfv 5888 |
. . . . . 6
class
(join‘𝑝) |
6 | 5 | cdm 5114 |
. . . . 5
class dom
(join‘𝑝) |
7 | | cbs 15857 |
. . . . . . 7
class
Base |
8 | 3, 7 | cfv 5888 |
. . . . . 6
class
(Base‘𝑝) |
9 | 8, 8 | cxp 5112 |
. . . . 5
class
((Base‘𝑝)
× (Base‘𝑝)) |
10 | 6, 9 | wceq 1483 |
. . . 4
wff dom
(join‘𝑝) =
((Base‘𝑝) ×
(Base‘𝑝)) |
11 | | cmee 16945 |
. . . . . . 7
class
meet |
12 | 3, 11 | cfv 5888 |
. . . . . 6
class
(meet‘𝑝) |
13 | 12 | cdm 5114 |
. . . . 5
class dom
(meet‘𝑝) |
14 | 13, 9 | wceq 1483 |
. . . 4
wff dom
(meet‘𝑝) =
((Base‘𝑝) ×
(Base‘𝑝)) |
15 | 10, 14 | wa 384 |
. . 3
wff (dom
(join‘𝑝) =
((Base‘𝑝) ×
(Base‘𝑝)) ∧ dom
(meet‘𝑝) =
((Base‘𝑝) ×
(Base‘𝑝))) |
16 | | cpo 16940 |
. . 3
class
Poset |
17 | 15, 2, 16 | crab 2916 |
. 2
class {𝑝 ∈ Poset ∣ (dom
(join‘𝑝) =
((Base‘𝑝) ×
(Base‘𝑝)) ∧ dom
(meet‘𝑝) =
((Base‘𝑝) ×
(Base‘𝑝)))} |
18 | 1, 17 | wceq 1483 |
1
wff Lat =
{𝑝 ∈ Poset ∣
(dom (join‘𝑝) =
((Base‘𝑝) ×
(Base‘𝑝)) ∧ dom
(meet‘𝑝) =
((Base‘𝑝) ×
(Base‘𝑝)))} |