Theorem prmm2nn0

Description: Subtracting 2 from a prime number results in a nonnegative integer. (Contributed by Alexander van der Vekens, 30-Aug-2018)

	Ref	Expression
Assertion	prmm2nn0	$$⊢P\in \mathbb{P}\to P-2\in {\mathbb{N}}_0$$

Proof

Step	Hyp	Ref	Expression
1		prmuz2	$$⊢P\in \mathbb{P}\to P\in {\mathbb{Z}}_{\ge 2}$$
2		uznn0sub	$$⊢P\in {\mathbb{Z}}_{\ge 2}\to P-2\in {\mathbb{N}}_0$$
3	1 2	syl	$$⊢P\in \mathbb{P}\to P-2\in {\mathbb{N}}_0$$