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Metamath Proof Explorer

Theorem 7lt10

Description: 7 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015) (Revised by AV, 8-Sep-2021)

Ref Expression
Assertion 7lt10 ⊢ 7 < 10

Proof

Step Hyp Ref Expression
1 7lt8 ⊢ 7 < 8
2 8lt10 ⊢ 8 < 10
3 7re ⊢ 7 ∈ ℝ
4 8re ⊢ 8 ∈ ℝ
5 10re ⊢ 10 ∈ ℝ
6 3 4 5 lttri ⊢ 7 < 8 ∧ 8 < 10 → 7 < 10
7 1 2 6 mp2an ⊢ 7 < 10