Theorem 6lt8

Description: 6 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	6lt8	$$⊢6<8$$

Proof

Step	Hyp	Ref	Expression
1		6lt7	$$⊢6<7$$
2		7lt8	$$⊢7<8$$
3		6re	$$⊢6\in ℝ$$
4		7re	$$⊢7\in ℝ$$
5		8re	$$⊢8\in ℝ$$
6	3 4 5	lttri	$$⊢\left(6<7\wedge 7<8\right)\to 6<8$$
7	1 2 6	mp2an	$$⊢6<8$$