Theorem sqge0d

Description: The square of a real is nonnegative, deduction form. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypothesis	sqge0d.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	sqge0d	⊢ ( 𝜑 → 0 ≤ ( 𝐴 ↑ 2 ) )

Proof

Step	Hyp	Ref	Expression
1		sqge0d.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		sqge0	⊢ ( 𝐴 ∈ ℝ → 0 ≤ ( 𝐴 ↑ 2 ) )
3	1 2	syl	⊢ ( 𝜑 → 0 ≤ ( 𝐴 ↑ 2 ) )