Theorem 2exp6

Description: Two to the sixth power is 64. (Contributed by Mario Carneiro, 20-Apr-2015) (Proof shortened by OpenAI, 25-Mar-2020)

	Ref	Expression
Assertion	2exp6	$$⊢2^6=64$$

Proof

Step	Hyp	Ref	Expression
1		2nn0	$$⊢2\in {\mathbb{N}}_0$$
2		3nn0	$$⊢3\in {\mathbb{N}}_0$$
3		3cn	$$⊢3\in ℂ$$
4		2cn	$$⊢2\in ℂ$$
5		3t2e6	$$⊢3\cdot 2=6$$
6	3 4 5	mulcomli	$$⊢2\cdot 3=6$$
7		cu2	$$⊢2^3=8$$
8		8t8e64	$$⊢8\cdot 8=64$$
9	1 2 6 7 8	numexp2x	$$⊢2^6=64$$