Theorem 4lt8

Description: 4 is less than 8. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	4lt8	$$⊢4<8$$

Proof

Step	Hyp	Ref	Expression
1		4lt5	$$⊢4<5$$
2		5lt8	$$⊢5<8$$
3		4re	$$⊢4\in ℝ$$
4		5re	$$⊢5\in ℝ$$
5		8re	$$⊢8\in ℝ$$
6	3 4 5	lttri	$$⊢\left(4<5\wedge 5<8\right)\to 4<8$$
7	1 2 6	mp2an	$$⊢4<8$$