Theorem nn0addge1i

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	$$⊢A\in ℝ$$
	nn0addge1i.2	$$⊢N\in {\mathbb{N}}_0$$
Assertion	nn0addge1i	$$⊢A\le A+N$$

Proof

Step	Hyp	Ref	Expression
1		nn0addge1i.1	$$⊢A\in ℝ$$
2		nn0addge1i.2	$$⊢N\in {\mathbb{N}}_0$$
3		nn0addge1	$$⊢\left(A\in ℝ\wedge N\in {\mathbb{N}}_0\right)\to A\le A+N$$
4	1 2 3	mp2an	$$⊢A\le A+N$$