Theorem 7p5e12

Description: 7 + 5 = 12. (Contributed by Mario Carneiro, 19-Apr-2015)

	Ref	Expression
Assertion	7p5e12	$$⊢7+5=12$$

Proof

Step	Hyp	Ref	Expression
1		7nn0	$$⊢7\in {\mathbb{N}}_0$$
2		4nn0	$$⊢4\in {\mathbb{N}}_0$$
3		1nn0	$$⊢1\in {\mathbb{N}}_0$$
4		df-5	$$⊢5=4+1$$
5		df-2	$$⊢2=1+1$$
6		7p4e11	$$⊢7+4=11$$
7	1 2 3 4 5 6	6p5lem	$$⊢7+5=12$$