Metamath Proof Explorer


Theorem 3lt6

Description: 3 is less than 6. (Contributed by Mario Carneiro, 15-Sep-2013)

Ref Expression
Assertion 3lt6 3 < 6

Proof

Step Hyp Ref Expression
1 3lt4 3 < 4
2 4lt6 4 < 6
3 3re 3 ∈ ℝ
4 4re 4 ∈ ℝ
5 6re 6 ∈ ℝ
6 3 4 5 lttri ( ( 3 < 4 ∧ 4 < 6 ) → 3 < 6 )
7 1 2 6 mp2an 3 < 6