Metamath Proof Explorer
Description: A function that maps a set x to the smallest Tarski class that
contains the set. (Contributed by FL, 30-Dec-2010)
|
|
Ref |
Expression |
|
Assertion |
df-tskm |
⊢ tarskiMap = ( 𝑥 ∈ V ↦ ∩ { 𝑦 ∈ Tarski ∣ 𝑥 ∈ 𝑦 } ) |
Detailed syntax breakdown
Step |
Hyp |
Ref |
Expression |
0 |
|
ctskm |
⊢ tarskiMap |
1 |
|
vx |
⊢ 𝑥 |
2 |
|
cvv |
⊢ V |
3 |
|
vy |
⊢ 𝑦 |
4 |
|
ctsk |
⊢ Tarski |
5 |
1
|
cv |
⊢ 𝑥 |
6 |
3
|
cv |
⊢ 𝑦 |
7 |
5 6
|
wcel |
⊢ 𝑥 ∈ 𝑦 |
8 |
7 3 4
|
crab |
⊢ { 𝑦 ∈ Tarski ∣ 𝑥 ∈ 𝑦 } |
9 |
8
|
cint |
⊢ ∩ { 𝑦 ∈ Tarski ∣ 𝑥 ∈ 𝑦 } |
10 |
1 2 9
|
cmpt |
⊢ ( 𝑥 ∈ V ↦ ∩ { 𝑦 ∈ Tarski ∣ 𝑥 ∈ 𝑦 } ) |
11 |
0 10
|
wceq |
⊢ tarskiMap = ( 𝑥 ∈ V ↦ ∩ { 𝑦 ∈ Tarski ∣ 𝑥 ∈ 𝑦 } ) |