Theorem 1nuz2

Description: 1 is not in ( ZZ>=2 ) . (Contributed by Paul Chapman, 21-Nov-2012)

	Ref	Expression
Assertion	1nuz2	$$⊢\neg 1\in {\mathbb{Z}}_{\ge 2}$$

Proof

Step	Hyp	Ref	Expression
1		neirr	$$⊢\neg 1\ne 1$$
2		eluz2b3	$$⊢1\in {\mathbb{Z}}_{\ge 2}\leftrightarrow \left(1\in \mathbb{N}\wedge 1\ne 1\right)$$
3	2	simprbi	$$⊢1\in {\mathbb{Z}}_{\ge 2}\to 1\ne 1$$
4	1 3	mto	$$⊢\neg 1\in {\mathbb{Z}}_{\ge 2}$$