Theorem 6lt9

Description: 6 is less than 9. (Contributed by Mario Carneiro, 9-Mar-2015)

	Ref	Expression
Assertion	6lt9	$$⊢6<9$$

Proof

Step	Hyp	Ref	Expression
1		6lt7	$$⊢6<7$$
2		7lt9	$$⊢7<9$$
3		6re	$$⊢6\in ℝ$$
4		7re	$$⊢7\in ℝ$$
5		9re	$$⊢9\in ℝ$$
6	3 4 5	lttri	$$⊢\left(6<7\wedge 7<9\right)\to 6<9$$
7	1 2 6	mp2an	$$⊢6<9$$