Theorem leabsd

Description: A real number is less than or equal to its absolute value. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	resqrcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	leabsd	⊢ ( 𝜑 → 𝐴 ≤ ( abs ‘ 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		resqrcld.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		leabs	⊢ ( 𝐴 ∈ ℝ → 𝐴 ≤ ( abs ‘ 𝐴 ) )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ≤ ( abs ‘ 𝐴 ) )