Users' Mathboxes Mathbox for Stefan O'Rear < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  df-squarenn Structured version   Visualization version   GIF version

Definition df-squarenn 39316
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
StepHypRef Expression
1 csquarenn 39311 . 2 class NN
2 vx . . . . . 6 setvar 𝑥
32cv 1527 . . . . 5 class 𝑥
4 csqrt 14580 . . . . 5 class
53, 4cfv 6348 . . . 4 class (√‘𝑥)
6 cq 12336 . . . 4 class
75, 6wcel 2105 . . 3 wff (√‘𝑥) ∈ ℚ
8 cn 11626 . . 3 class
97, 2, 8crab 3139 . 2 class {𝑥 ∈ ℕ ∣ (√‘𝑥) ∈ ℚ}
101, 9wceq 1528 1 wff NN = {𝑥 ∈ ℕ ∣ (√‘𝑥) ∈ ℚ}
Colors of variables: wff setvar class
This definition is referenced by:  pellqrex  39354  rmspecnonsq  39382
  Copyright terms: Public domain W3C validator