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	$$⊢\neg 10\in \mathbb{P}$$

Proof

Step	Hyp	Ref	Expression
1		1nn	$$⊢1\in \mathbb{N}$$
2		0nn0	$$⊢0\in {\mathbb{N}}_0$$
3		2cn	$$⊢2\in ℂ$$
4	3	mul02i	$$⊢0\cdot 2=0$$
5	1 2 4	dec2nprm	$$⊢\neg 10\in \mathbb{P}$$