Theorem 6lt10

Description: 6 is less than 10. (Contributed by Mario Carneiro, 10-Mar-2015) (Revised by AV, 8-Sep-2021)

	Ref	Expression
Assertion	6lt10	⊢ 6 < ; 1 0

Proof

Step	Hyp	Ref	Expression
1		6lt7	⊢ 6 < 7
2		7lt10	⊢ 7 < ; 1 0
3		6re	⊢ 6 ∈ ℝ
4		7re	⊢ 7 ∈ ℝ
5		10re	⊢ ; 1 0 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 6 < 7 ∧ 7 < ; 1 0 ) → 6 < ; 1 0 )
7	1 2 6	mp2an	⊢ 6 < ; 1 0