Theorem 2lt8

Description: 2 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	2lt8	$$⊢2<8$$

Proof

Step	Hyp	Ref	Expression
1		2lt3	$$⊢2<3$$
2		3lt8	$$⊢3<8$$
3		2re	$$⊢2\in ℝ$$
4		3re	$$⊢3\in ℝ$$
5		8re	$$⊢8\in ℝ$$
6	3 4 5	lttri	$$⊢\left(2<3\wedge 3<8\right)\to 2<8$$
7	1 2 6	mp2an	$$⊢2<8$$