Theorem nn0sub2

Description: Subtraction of nonnegative integers. (Contributed by NM, 4-Sep-2005)

	Ref	Expression
Assertion	nn0sub2	$$⊢\left(M\in {\mathbb{N}}_0\wedge N\in {\mathbb{N}}_0\wedge M\le N\right)\to N-M\in {\mathbb{N}}_0$$

Proof

Step	Hyp	Ref	Expression
1		nn0sub	$$⊢\left(M\in {\mathbb{N}}_0\wedge N\in {\mathbb{N}}_0\right)\to \left(M\le N\leftrightarrow N-M\in {\mathbb{N}}_0\right)$$
2	1	biimp3a	$$⊢\left(M\in {\mathbb{N}}_0\wedge N\in {\mathbb{N}}_0\wedge M\le N\right)\to N-M\in {\mathbb{N}}_0$$