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 e. RR
4		6re	|- 6 e. RR
5		7re	|- 7 e. RR
6	3 4 5	lttri	|- ( ( 5 < 6 /\ 6 < 7 ) -> 5 < 7 )
7	1 2 6	mp2an	|- 5 < 7