Metamath Proof Explorer


Definition df-even

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
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 }