Definition df-squarenn 42852

Description: Define the set of square positive integers. (Contributed by Stefan O'Rear, 18-Sep-2014.)

Assertion

Ref	Expression
df-squarenn	⊢ ◻NN = {𝑥 ∈ ℕ ∣ (√‘𝑥) ∈ ℚ}

Detailed syntax breakdown of Definition df-squarenn

Step	Hyp	Ref	Expression
1		csquarenn 42847	. 2 class ◻NN
2		vx	. . . . . 6 setvar 𝑥
3	2	cv 1539	. . . . 5 class 𝑥
4		csqrt 15272	. . . . 5 class √
5	3, 4	cfv 6561	. . . 4 class (√‘𝑥)
6		cq 12990	. . . 4 class ℚ
7	5, 6	wcel 2108	. . 3 wff (√‘𝑥) ∈ ℚ
8		cn 12266	. . 3 class ℕ
9	7, 2, 8	crab 3436	. 2 class {𝑥 ∈ ℕ ∣ (√‘𝑥) ∈ ℚ}
10	1, 9	wceq 1540	1 wff ◻NN = {𝑥 ∈ ℕ ∣ (√‘𝑥) ∈ ℚ}

This definition is referenced by:  pellqrex  42890  rmspecnonsq  42918