Metamath Proof Explorer
Description: Define the set of even numbers. (Contributed by AV, 14-Jun-2020)
|
|
Ref |
Expression |
|
Assertion |
df-even |
⊢ Even = { 𝑧 ∈ ℤ ∣ ( 𝑧 / 2 ) ∈ ℤ } |
Detailed syntax breakdown
Step |
Hyp |
Ref |
Expression |
0 |
|
ceven |
⊢ Even |
1 |
|
vz |
⊢ 𝑧 |
2 |
|
cz |
⊢ ℤ |
3 |
1
|
cv |
⊢ 𝑧 |
4 |
|
cdiv |
⊢ / |
5 |
|
c2 |
⊢ 2 |
6 |
3 5 4
|
co |
⊢ ( 𝑧 / 2 ) |
7 |
6 2
|
wcel |
⊢ ( 𝑧 / 2 ) ∈ ℤ |
8 |
7 1 2
|
crab |
⊢ { 𝑧 ∈ ℤ ∣ ( 𝑧 / 2 ) ∈ ℤ } |
9 |
0 8
|
wceq |
⊢ Even = { 𝑧 ∈ ℤ ∣ ( 𝑧 / 2 ) ∈ ℤ } |