Theorem 8p5e13

Description: 8 + 5 = 13. (Contributed by Mario Carneiro, 19-Apr-2015)

	Ref	Expression
Assertion	8p5e13	$$⊢8+5=13$$

Proof

Step	Hyp	Ref	Expression
1		8nn0	$$⊢8\in {\mathbb{N}}_0$$
2		4nn0	$$⊢4\in {\mathbb{N}}_0$$
3		2nn0	$$⊢2\in {\mathbb{N}}_0$$
4		df-5	$$⊢5=4+1$$
5		df-3	$$⊢3=2+1$$
6		8p4e12	$$⊢8+4=12$$
7	1 2 3 4 5 6	6p5lem	$$⊢8+5=13$$