Metamath Proof Explorer


Theorem msqge0d

Description: A square is nonnegative. (Contributed by Mario Carneiro, 27-May-2016)

Ref Expression
Hypothesis leidd.1 ⊢ φ → A ∈ ℝ
Assertion msqge0d ⊢ φ → 0 ≤ A ⁢ A

Proof

Step Hyp Ref Expression
1 leidd.1 ⊢ φ → A ∈ ℝ
2 msqge0 ⊢ A ∈ ℝ → 0 ≤ A ⁢ A
3 1 2 syl ⊢ φ → 0 ≤ A ⁢ A