Description: The square root of a positive real is positive. (Contributed by NM, 26-May-1999) (Revised by Mario Carneiro, 6-Sep-2013)
Ref | Expression | ||
---|---|---|---|
Hypothesis | sqrtthi.1 | ⊢ 𝐴 ∈ ℝ | |
Assertion | sqrtgt0i | ⊢ ( 0 < 𝐴 → 0 < ( √ ‘ 𝐴 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sqrtthi.1 | ⊢ 𝐴 ∈ ℝ | |
2 | sqrtgt0 | ⊢ ( ( 𝐴 ∈ ℝ ∧ 0 < 𝐴 ) → 0 < ( √ ‘ 𝐴 ) ) | |
3 | 1 2 | mpan | ⊢ ( 0 < 𝐴 → 0 < ( √ ‘ 𝐴 ) ) |