Theorem nn0le2xi

Description: A nonnegative integer is less than or equal to twice itself. (Contributed by Raph Levien, 10-Dec-2002)

	Ref	Expression
Hypothesis	nn0le2xi.1	⊢ 𝑁 ∈ ℕ0
Assertion	nn0le2xi	⊢ 𝑁 ≤ ( 2 · 𝑁 )

Proof

Step	Hyp	Ref	Expression
1		nn0le2xi.1	⊢ 𝑁 ∈ ℕ0
2	1	nn0rei	⊢ 𝑁 ∈ ℝ
3	2 1	nn0addge1i	⊢ 𝑁 ≤ ( 𝑁 + 𝑁 )
4	1	nn0cni	⊢ 𝑁 ∈ ℂ
5	4	2timesi	⊢ ( 2 · 𝑁 ) = ( 𝑁 + 𝑁 )
6	3 5	breqtrri	⊢ 𝑁 ≤ ( 2 · 𝑁 )