Theorem 1lt3

Description: 1 is less than 3. (Contributed by NM, 26-Sep-2010)

	Ref	Expression
Assertion	1lt3	|- 1 < 3

Proof

Step	Hyp	Ref	Expression
1		1lt2	|- 1 < 2
2		2lt3	|- 2 < 3
3		1re	|- 1 e. RR
4		2re	|- 2 e. RR
5		3re	|- 3 e. RR
6	3 4 5	lttri	|- ( ( 1 < 2 /\ 2 < 3 ) -> 1 < 3 )
7	1 2 6	mp2an	|- 1 < 3