Description: The square of a nonzero real is positive. (Contributed by NM, 17-Sep-1999)
Ref | Expression | ||
---|---|---|---|
Hypothesis | resqcl.1 | ⊢ 𝐴 ∈ ℝ | |
Assertion | sqgt0i | ⊢ ( 𝐴 ≠ 0 → 0 < ( 𝐴 ↑ 2 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | resqcl.1 | ⊢ 𝐴 ∈ ℝ | |
2 | sqgt0 | ⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐴 ≠ 0 ) → 0 < ( 𝐴 ↑ 2 ) ) | |
3 | 1 2 | mpan | ⊢ ( 𝐴 ≠ 0 → 0 < ( 𝐴 ↑ 2 ) ) |