Theorem 1lt3

Description: 1 is less than 3. (Contributed by NM, 26-Sep-2010)

	Ref	Expression
Assertion	1lt3	$$⊢1<3$$

Proof

Step	Hyp	Ref	Expression
1		1lt2	$$⊢1<2$$
2		2lt3	$$⊢2<3$$
3		1re	$$⊢1\in ℝ$$
4		2re	$$⊢2\in ℝ$$
5		3re	$$⊢3\in ℝ$$
6	3 4 5	lttri	$$⊢\left(1<2\wedge 2<3\right)\to 1<3$$
7	1 2 6	mp2an	$$⊢1<3$$