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Mirrors > Home > MPE Home > Th. List > Mathboxes > df-squarenn | Structured version Visualization version GIF version |
Description: Define the set of square positive integers. (Contributed by Stefan O'Rear, 18-Sep-2014.) |
Ref | Expression |
---|---|
df-squarenn | ⊢ ◻NN = {𝑥 ∈ ℕ ∣ (√‘𝑥) ∈ ℚ} |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csquarenn 37400 | . 2 class ◻NN | |
2 | vx | . . . . . 6 setvar 𝑥 | |
3 | 2 | cv 1482 | . . . . 5 class 𝑥 |
4 | csqrt 13973 | . . . . 5 class √ | |
5 | 3, 4 | cfv 5888 | . . . 4 class (√‘𝑥) |
6 | cq 11788 | . . . 4 class ℚ | |
7 | 5, 6 | wcel 1990 | . . 3 wff (√‘𝑥) ∈ ℚ |
8 | cn 11020 | . . 3 class ℕ | |
9 | 7, 2, 8 | crab 2916 | . 2 class {𝑥 ∈ ℕ ∣ (√‘𝑥) ∈ ℚ} |
10 | 1, 9 | wceq 1483 | 1 wff ◻NN = {𝑥 ∈ ℕ ∣ (√‘𝑥) ∈ ℚ} |
Colors of variables: wff setvar class |
This definition is referenced by: pellqrex 37443 rmspecnonsq 37472 |
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