Metamath Proof Explorer


Theorem 3lt9

Description: 3 is less than 9. (Contributed by Mario Carneiro, 9-Mar-2015)

Ref Expression
Assertion 3lt9 ⊢ 3 < 9

Proof

Step Hyp Ref Expression
1 3lt4 ⊢ 3 < 4
2 4lt9 ⊢ 4 < 9
3 3re ⊢ 3 ∈ ℝ
4 4re ⊢ 4 ∈ ℝ
5 9re ⊢ 9 ∈ ℝ
6 3 4 5 lttri ⊢ 3 < 4 ∧ 4 < 9 → 3 < 9
7 1 2 6 mp2an ⊢ 3 < 9