Theorem 2lt5

Description: 2 is less than 5. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	2lt5	$$⊢2<5$$

Proof

Step	Hyp	Ref	Expression
1		2lt4	$$⊢2<4$$
2		4lt5	$$⊢4<5$$
3		2re	$$⊢2\in ℝ$$
4		4re	$$⊢4\in ℝ$$
5		5re	$$⊢5\in ℝ$$
6	3 4 5	lttri	$$⊢\left(2<4\wedge 4<5\right)\to 2<5$$
7	1 2 6	mp2an	$$⊢2<5$$