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 class Even
1 vz setvar z
2 cz class ℤ
3 1 cv setvar z
4 cdiv class ÷
5 c2 class 2
6 3 5 4 co class z 2
7 6 2 wcel wff z 2 ∈ ℤ
8 7 1 2 crab class z ∈ ℤ | z 2 ∈ ℤ
9 0 8 wceq wff Even = z ∈ ℤ | z 2 ∈ ℤ