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 e. RR
	nn0addge1i.2	|- N e. NN0
Assertion	nn0addge2i	|- A <_ ( N + A )

Proof

Step	Hyp	Ref	Expression
1		nn0addge1i.1	|- A e. RR
2		nn0addge1i.2	|- N e. NN0
3		nn0addge2	|- ( ( A e. RR /\ N e. NN0 ) -> A <_ ( N + A ) )
4	1 2 3	mp2an	|- A <_ ( N + A )