Theorem 5lt7

Description: 5 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	5lt7	$$⊢5<7$$

Proof

Step	Hyp	Ref	Expression
1		5lt6	$$⊢5<6$$
2		6lt7	$$⊢6<7$$
3		5re	$$⊢5\in ℝ$$
4		6re	$$⊢6\in ℝ$$
5		7re	$$⊢7\in ℝ$$
6	3 4 5	lttri	$$⊢\left(5<6\wedge 6<7\right)\to 5<7$$
7	1 2 6	mp2an	$$⊢5<7$$