Metamath Proof Explorer


Theorem fmtno2prm

Description: The 2 nd Fermat number is a prime (_third Fermat prime_). (Contributed by AV, 13-Jun-2021)

Ref Expression
Assertion fmtno2prm ⊢ FermatNo ⁡ 2 ∈ ℙ

Proof

Step Hyp Ref Expression
1 fmtno2 ⊢ FermatNo ⁡ 2 = 17
2 17prm ⊢ 17 ∈ ℙ
3 1 2 eqeltri ⊢ FermatNo ⁡ 2 ∈ ℙ