Theorem 10nprm

Description: 10 is not a prime number. (Contributed by Mario Carneiro, 18-Feb-2014) (Revised by AV, 6-Sep-2021) (Proof shortened by Umit Teoman Dogan, 10-Jun-2026)

	Ref	Expression
Assertion	10nprm	⊢ ¬ ; 1 0 ∈ ℙ

Proof

Step	Hyp	Ref	Expression
1		1nn	⊢ 1 ∈ ℕ
2		0nn0	⊢ 0 ∈ ℕ0
3		2cn	⊢ 2 ∈ ℂ
4	3	mul02i	⊢ ( 0 · 2 ) = 0
5	1 2 4	dec2nprm	⊢ ¬ ; 1 0 ∈ ℙ