Theorem sqgt0i

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 ) )

Proof

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 ) )