Theorem 3exp3

Description: Three to the third power is 27. (Contributed by Mario Carneiro, 20-Apr-2015)

	Ref	Expression
Assertion	3exp3	$$⊢3^3=27$$

Proof

Step	Hyp	Ref	Expression
1		3nn0	$$⊢3\in {\mathbb{N}}_0$$
2		2nn0	$$⊢2\in {\mathbb{N}}_0$$
3		2p1e3	$$⊢2+1=3$$
4		sq3	$$⊢3^2=9$$
5	4	oveq1i	$$⊢3^2\cdot 3=9\cdot 3$$
6		9t3e27	$$⊢9\cdot 3=27$$
7	5 6	eqtri	$$⊢3^2\cdot 3=27$$
8	1 2 3 7	numexpp1	$$⊢3^3=27$$