Theorem 2eluzge1

Description: 2 is an integer greater than or equal to 1. (Contributed by Alexander van der Vekens, 8-Jun-2018)

	Ref	Expression
Assertion	2eluzge1	$$⊢2\in {\mathbb{Z}}_{\ge 1}$$

Proof

Step	Hyp	Ref	Expression
1		1z	$$⊢1\in \mathbb{Z}$$
2		2z	$$⊢2\in \mathbb{Z}$$
3		1le2	$$⊢1\le 2$$
4		eluz2	$$⊢2\in {\mathbb{Z}}_{\ge 1}\leftrightarrow \left(1\in \mathbb{Z}\wedge 2\in \mathbb{Z}\wedge 1\le 2\right)$$
5	1 2 3 4	mpbir3an	$$⊢2\in {\mathbb{Z}}_{\ge 1}$$