Theorem sq45

Description: 45 squared is 2025. (Contributed by SN, 30-Mar-2025)

	Ref	Expression
Assertion	sq45	$$⊢{45}^2=2025$$

Proof

Step	Hyp	Ref	Expression
1		4nn0	$$⊢4\in {\mathbb{N}}_0$$
2		5nn0	$$⊢5\in {\mathbb{N}}_0$$
3	1 2	deccl	$$⊢45\in {\mathbb{N}}_0$$
4	3	nn0cni	$$⊢45\in ℂ$$
5	4	sqvali	$$⊢{45}^2=45\cdot 45$$
6		4p1e5	$$⊢4+1=5$$
7		4t5e20	$$⊢4\cdot 5=20$$
8	1 6 7	sqn5ii	$$⊢45\cdot 45=2025$$
9	5 8	eqtri	$$⊢{45}^2=2025$$