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 ∈ ℝ
4		2re	⊢ 2 ∈ ℝ
5		3re	⊢ 3 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 1 < 2 ∧ 2 < 3 ) → 1 < 3 )
7	1 2 6	mp2an	⊢ 1 < 3