Theorem 1lt8

Description: 1 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	1lt8	$$⊢1<8$$

Proof

Step	Hyp	Ref	Expression
1		1lt2	$$⊢1<2$$
2		2lt8	$$⊢2<8$$
3		1re	$$⊢1\in ℝ$$
4		2re	$$⊢2\in ℝ$$
5		8re	$$⊢8\in ℝ$$
6	3 4 5	lttri	$$⊢\left(1<2\wedge 2<8\right)\to 1<8$$
7	1 2 6	mp2an	$$⊢1<8$$