Metamath Proof Explorer


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