Theorem prmuz2

Description: A prime number is an integer greater than or equal to 2. (Contributed by Paul Chapman, 17-Nov-2012)

	Ref	Expression
Assertion	prmuz2	$$⊢P\in \mathbb{P}\to P\in {\mathbb{Z}}_{\ge 2}$$

Proof

Step	Hyp	Ref	Expression
1		isprm4	$$⊢P\in \mathbb{P}\leftrightarrow \left(P\in {\mathbb{Z}}_{\ge 2}\wedge \forall x\in {\mathbb{Z}}_{\ge 2}\left(x\parallel P\to x=P\right)\right)$$
2	1	simplbi	$$⊢P\in \mathbb{P}\to P\in {\mathbb{Z}}_{\ge 2}$$