Theorem 3lt7

Description: 3 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	3lt7	|- 3 < 7

Proof

Step	Hyp	Ref	Expression
1		3lt4	|- 3 < 4
2		4lt7	|- 4 < 7
3		3re	|- 3 e. RR
4		4re	|- 4 e. RR
5		7re	|- 7 e. RR
6	3 4 5	lttri	|- ( ( 3 < 4 /\ 4 < 7 ) -> 3 < 7 )
7	1 2 6	mp2an	|- 3 < 7