Description: The square of a real is nonnegative. (Contributed by NM, 3-Aug-1999)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | resqcl.1 | ⊢ 𝐴 ∈ ℝ | |
| Assertion | sqge0i | ⊢ 0 ≤ ( 𝐴 ↑ 2 ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | resqcl.1 | ⊢ 𝐴 ∈ ℝ | |
| 2 | 1 | msqge0i | ⊢ 0 ≤ ( 𝐴 · 𝐴 ) |
| 3 | 1 | recni | ⊢ 𝐴 ∈ ℂ |
| 4 | 3 | sqvali | ⊢ ( 𝐴 ↑ 2 ) = ( 𝐴 · 𝐴 ) |
| 5 | 2 4 | breqtrri | ⊢ 0 ≤ ( 𝐴 ↑ 2 ) |