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 < ; 1 0

Proof

Step	Hyp	Ref	Expression
1		8lt9	⊢ 8 < 9
2		9lt10	⊢ 9 < ; 1 0
3		8re	⊢ 8 ∈ ℝ
4		9re	⊢ 9 ∈ ℝ
5		10re	⊢ ; 1 0 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 8 < 9 ∧ 9 < ; 1 0 ) → 8 < ; 1 0 )
7	1 2 6	mp2an	⊢ 8 < ; 1 0