Definition df-even 40077

Description: Define the set of even numbers. (Contributed by AV, 14-Jun-2020.)

Assertion

Ref	Expression
df-even	⊢ Even = {𝑧 ∈ ℤ ∣ (𝑧 / 2) ∈ ℤ}

Detailed syntax breakdown of Definition df-even

Step	Hyp	Ref	Expression
1		ceven 40075	. 2 class Even
2		vz	. . . . . 6 setvar 𝑧
3	2	cv 1474	. . . . 5 class 𝑧
4		c2 10947	. . . . 5 class 2
5		cdiv 10563	. . . . 5 class /
6	3, 4, 5	co 6549	. . . 4 class (𝑧 / 2)
7		cz 11254	. . . 4 class ℤ
8	6, 7	wcel 1977	. . 3 wff (𝑧 / 2) ∈ ℤ
9	8, 2, 7	crab 2900	. 2 class {𝑧 ∈ ℤ ∣ (𝑧 / 2) ∈ ℤ}
10	1, 9	wceq 1475	1 wff Even = {𝑧 ∈ ℤ ∣ (𝑧 / 2) ∈ ℤ}

This definition is referenced by:  iseven  40079  dfeven4  40089  dfeven3  40108