Theorem 2lt7

Description: 2 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	2lt7	⊢ 2 < 7

Proof

Step	Hyp	Ref	Expression
1		2lt3	⊢ 2 < 3
2		3lt7	⊢ 3 < 7
3		2re	⊢ 2 ∈ ℝ
4		3re	⊢ 3 ∈ ℝ
5		7re	⊢ 7 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 2 < 3 ∧ 3 < 7 ) → 2 < 7 )
7	1 2 6	mp2an	⊢ 2 < 7