Theorem nn0addge2i

Description: A number is less than or equal to itself plus a nonnegative integer. (Contributed by NM, 10-Mar-2005)

	Ref	Expression
Hypotheses	nn0addge1i.1	⊢ 𝐴 ∈ ℝ
	nn0addge1i.2	⊢ 𝑁 ∈ ℕ0
Assertion	nn0addge2i	⊢ 𝐴 ≤ ( 𝑁 + 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		nn0addge1i.1	⊢ 𝐴 ∈ ℝ
2		nn0addge1i.2	⊢ 𝑁 ∈ ℕ0
3		nn0addge2	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝑁 ∈ ℕ0 ) → 𝐴 ≤ ( 𝑁 + 𝐴 ) )
4	1 2 3	mp2an	⊢ 𝐴 ≤ ( 𝑁 + 𝐴 )