Theorem 2lt7

Description: 2 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	2lt7	$$⊢2<7$$

Proof

Step	Hyp	Ref	Expression
1		2lt3	$$⊢2<3$$
2		3lt7	$$⊢3<7$$
3		2re	$$⊢2\in ℝ$$
4		3re	$$⊢3\in ℝ$$
5		7re	$$⊢7\in ℝ$$
6	3 4 5	lttri	$$⊢\left(2<3\wedge 3<7\right)\to 2<7$$
7	1 2 6	mp2an	$$⊢2<7$$