Theorem 4lt7

Description: 4 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	4lt7	$$⊢4<7$$

Proof

Step	Hyp	Ref	Expression
1		4lt5	$$⊢4<5$$
2		5lt7	$$⊢5<7$$
3		4re	$$⊢4\in ℝ$$
4		5re	$$⊢5\in ℝ$$
5		7re	$$⊢7\in ℝ$$
6	3 4 5	lttri	$$⊢\left(4<5\wedge 5<7\right)\to 4<7$$
7	1 2 6	mp2an	$$⊢4<7$$