Theorem 2lt7

Description: 2 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	2lt7	|- 2 < 7

Proof

Step	Hyp	Ref	Expression
1		2lt3	|- 2 < 3
2		3lt7	|- 3 < 7
3		2re	|- 2 e. RR
4		3re	|- 3 e. RR
5		7re	|- 7 e. RR
6	3 4 5	lttri	|- ( ( 2 < 3 /\ 3 < 7 ) -> 2 < 7 )
7	1 2 6	mp2an	|- 2 < 7