Theorem 7lt10

Description: 7 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015) (Revised by AV, 8-Sep-2021)

	Ref	Expression
Assertion	7lt10	$$⊢7<10$$

Proof

Step	Hyp	Ref	Expression
1		7lt8	$$⊢7<8$$
2		8lt10	$$⊢8<10$$
3		7re	$$⊢7\in ℝ$$
4		8re	$$⊢8\in ℝ$$
5		10re	$$⊢10\in ℝ$$
6	3 4 5	lttri	$$⊢\left(7<8\wedge 8<10\right)\to 7<10$$
7	1 2 6	mp2an	$$⊢7<10$$