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 ∈ ℙ → 𝑃 ∈ ( ℤ≥ ‘ 2 ) )

Proof

Step	Hyp	Ref	Expression
1		isprm4	⊢ ( 𝑃 ∈ ℙ ↔ ( 𝑃 ∈ ( ℤ≥ ‘ 2 ) ∧ ∀ 𝑥 ∈ ( ℤ≥ ‘ 2 ) ( 𝑥 ∥ 𝑃 → 𝑥 = 𝑃 ) ) )
2	1	simplbi	⊢ ( 𝑃 ∈ ℙ → 𝑃 ∈ ( ℤ≥ ‘ 2 ) )