Metamath Proof Explorer


Theorem absge0d

Description: Absolute value is nonnegative. (Contributed by Mario Carneiro, 29-May-2016)

Ref Expression
Hypothesis abscld.1 ⊢ φ → A ∈ ℂ
Assertion absge0d ⊢ φ → 0 ≤ A

Proof

Step Hyp Ref Expression
1 abscld.1 ⊢ φ → A ∈ ℂ
2 absge0 ⊢ A ∈ ℂ → 0 ≤ A
3 1 2 syl ⊢ φ → 0 ≤ A