Theorem leabsi

Description: A real number is less than or equal to its absolute value. (Contributed by NM, 2-Aug-1999)

	Ref	Expression
Hypothesis	sqrtthi.1	⊢ 𝐴 ∈ ℝ
Assertion	leabsi	⊢ 𝐴 ≤ ( abs ‘ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		sqrtthi.1	⊢ 𝐴 ∈ ℝ
2		leabs	⊢ ( 𝐴 ∈ ℝ → 𝐴 ≤ ( abs ‘ 𝐴 ) )
3	1 2	ax-mp	⊢ 𝐴 ≤ ( abs ‘ 𝐴 )