Theorem 3lt7

Description: 3 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	3lt7	$$⊢3<7$$

Proof

Step	Hyp	Ref	Expression
1		3lt4	$$⊢3<4$$
2		4lt7	$$⊢4<7$$
3		3re	$$⊢3\in ℝ$$
4		4re	$$⊢4\in ℝ$$
5		7re	$$⊢7\in ℝ$$
6	3 4 5	lttri	$$⊢\left(3<4\wedge 4<7\right)\to 3<7$$
7	1 2 6	mp2an	$$⊢3<7$$