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 ∈ ℙ → ( 𝑃 − 2 ) ∈ ℕ0 )

Proof

Step	Hyp	Ref	Expression
1		prmuz2	⊢ ( 𝑃 ∈ ℙ → 𝑃 ∈ ( ℤ≥ ‘ 2 ) )
2		uznn0sub	⊢ ( 𝑃 ∈ ( ℤ≥ ‘ 2 ) → ( 𝑃 − 2 ) ∈ ℕ0 )
3	1 2	syl	⊢ ( 𝑃 ∈ ℙ → ( 𝑃 − 2 ) ∈ ℕ0 )