Theorem 9t5e45

Description: 9 times 5 equals 45. (Contributed by Mario Carneiro, 19-Apr-2015)

	Ref	Expression
Assertion	9t5e45	$$⊢9\cdot 5=45$$

Proof

Step	Hyp	Ref	Expression
1		9nn0	$$⊢9\in {\mathbb{N}}_0$$
2		4nn0	$$⊢4\in {\mathbb{N}}_0$$
3		df-5	$$⊢5=4+1$$
4		9t4e36	$$⊢9\cdot 4=36$$
5		3nn0	$$⊢3\in {\mathbb{N}}_0$$
6		6nn0	$$⊢6\in {\mathbb{N}}_0$$
7		eqid	$$⊢36=36$$
8		3p1e4	$$⊢3+1=4$$
9		5nn0	$$⊢5\in {\mathbb{N}}_0$$
10	1	nn0cni	$$⊢9\in ℂ$$
11	6	nn0cni	$$⊢6\in ℂ$$
12		9p6e15	$$⊢9+6=15$$
13	10 11 12	addcomli	$$⊢6+9=15$$
14	5 6 1 7 8 9 13	decaddci	$$⊢36+9=45$$
15	1 2 3 4 14	4t3lem	$$⊢9\cdot 5=45$$