Metamath Proof Explorer


Theorem 2lt9

Description: 2 is less than 9. (Contributed by Mario Carneiro, 9-Mar-2015)

Ref Expression
Assertion 2lt9 ⊢ 2 < 9

Proof

Step Hyp Ref Expression
1 2lt3 ⊢ 2 < 3
2 3lt9 ⊢ 3 < 9
3 2re ⊢ 2 ∈ ℝ
4 3re ⊢ 3 ∈ ℝ
5 9re ⊢ 9 ∈ ℝ
6 3 4 5 lttri ⊢ 2 < 3 ∧ 3 < 9 → 2 < 9
7 1 2 6 mp2an ⊢ 2 < 9