Theorem 5lt7

Description: 5 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	5lt7	⊢ 5 < 7

Proof

Step	Hyp	Ref	Expression
1		5lt6	⊢ 5 < 6
2		6lt7	⊢ 6 < 7
3		5re	⊢ 5 ∈ ℝ
4		6re	⊢ 6 ∈ ℝ
5		7re	⊢ 7 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 5 < 6 ∧ 6 < 7 ) → 5 < 7 )
7	1 2 6	mp2an	⊢ 5 < 7