Theorem msqge0i

Description: A square is nonnegative. (Contributed by NM, 14-May-1999) (Proof shortened by Andrew Salmon, 19-Nov-2011)

	Ref	Expression
Hypothesis	lt2.1	⊢ 𝐴 ∈ ℝ
Assertion	msqge0i	⊢ 0 ≤ ( 𝐴 · 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		lt2.1	⊢ 𝐴 ∈ ℝ
2		msqge0	⊢ ( 𝐴 ∈ ℝ → 0 ≤ ( 𝐴 · 𝐴 ) )
3	1 2	ax-mp	⊢ 0 ≤ ( 𝐴 · 𝐴 )