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Metamath Proof Explorer

Theorem 8lt10

Description: 8 is less than 10. (Contributed by Mario Carneiro, 8-Feb-2015) (Revised by AV, 8-Sep-2021)

Ref Expression
Assertion 8lt10 ⊢ 8 < 10

Proof

Step Hyp Ref Expression
1 8lt9 ⊢ 8 < 9
2 9lt10 ⊢ 9 < 10
3 8re ⊢ 8 ∈ ℝ
4 9re ⊢ 9 ∈ ℝ
5 10re ⊢ 10 ∈ ℝ
6 3 4 5 lttri ⊢ 8 < 9 ∧ 9 < 10 → 8 < 10
7 1 2 6 mp2an ⊢ 8 < 10