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 } |