Theorem 4lt7

Description: 4 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	4lt7	|- 4 < 7

Proof

Step	Hyp	Ref	Expression
1		4lt5	|- 4 < 5
2		5lt7	|- 5 < 7
3		4re	|- 4 e. RR
4		5re	|- 5 e. RR
5		7re	|- 7 e. RR
6	3 4 5	lttri	|- ( ( 4 < 5 /\ 5 < 7 ) -> 4 < 7 )
7	1 2 6	mp2an	|- 4 < 7