Description: The absolute value of a nonzero number is positive. Remark in Apostol p. 363. (Contributed by NM, 1-Oct-1999)
Ref | Expression | ||
---|---|---|---|
Hypothesis | absvalsqi.1 | ⊢ 𝐴 ∈ ℂ | |
Assertion | absgt0i | ⊢ ( 𝐴 ≠ 0 ↔ 0 < ( abs ‘ 𝐴 ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | absvalsqi.1 | ⊢ 𝐴 ∈ ℂ | |
2 | absgt0 | ⊢ ( 𝐴 ∈ ℂ → ( 𝐴 ≠ 0 ↔ 0 < ( abs ‘ 𝐴 ) ) ) | |
3 | 1 2 | ax-mp | ⊢ ( 𝐴 ≠ 0 ↔ 0 < ( abs ‘ 𝐴 ) ) |