Theorem 4lt7

Description: 4 is less than 7. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	4lt7	⊢ 4 < 7

Proof

Step	Hyp	Ref	Expression
1		4lt5	⊢ 4 < 5
2		5lt7	⊢ 5 < 7
3		4re	⊢ 4 ∈ ℝ
4		5re	⊢ 5 ∈ ℝ
5		7re	⊢ 7 ∈ ℝ
6	3 4 5	lttri	⊢ ( ( 4 < 5 ∧ 5 < 7 ) → 4 < 7 )
7	1 2 6	mp2an	⊢ 4 < 7