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Metamath Proof Explorer

Theorem oddprmuzge3

Description: A prime number which is odd is an integer greater than or equal to 3. (Contributed by AV, 20-Jul-2020) (Proof shortened by AV, 21-Aug-2021)

Ref Expression
Assertion oddprmuzge3 ( ( 𝑃 ∈ ℙ ∧ 𝑃 ∈ Odd ) → 𝑃 ∈ ( ℤ≥ ‘ 3 ) )

Proof

Step Hyp Ref Expression
1 oddprmne2 ⊢ ( ( 𝑃 ∈ ℙ ∧ 𝑃 ∈ Odd ) ↔ 𝑃 ∈ ( ℙ ∖ { 2 } ) )
2 oddprmge3 ⊢ ( 𝑃 ∈ ( ℙ ∖ { 2 } ) → 𝑃 ∈ ( ℤ≥ ‘ 3 ) )
3 1 2 sylbi ⊢ ( ( 𝑃 ∈ ℙ ∧ 𝑃 ∈ Odd ) → 𝑃 ∈ ( ℤ≥ ‘ 3 ) )