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Metamath Proof Explorer

Theorem nn0addge1i

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

Step	Hyp	Ref	Expression
1		nn0addge1i.1	$⊢ A \in ℝ$
2		nn0addge1i.2	$⊢ N \in ℕ_{0}$
3		nn0addge1	$⊢ (A \in ℝ \land N \in ℕ_{0}) \to A \leq A + N$
4	1 2 3	mp2an	$⊢ A \leq A + N$