Theorem iiconn

Description: The unit interval is connected. (Contributed by Mario Carneiro, 11-Feb-2015)

	Ref	Expression
Assertion	iiconn	⊢ II ∈ Conn

Proof

Step	Hyp	Ref	Expression
1		dfii2	⊢ II = ( ( topGen ‘ ran (,) ) ↾t ( 0 [,] 1 ) )
2		0re	⊢ 0 ∈ ℝ
3		1re	⊢ 1 ∈ ℝ
4		iccconn	⊢ ( ( 0 ∈ ℝ ∧ 1 ∈ ℝ ) → ( ( topGen ‘ ran (,) ) ↾t ( 0 [,] 1 ) ) ∈ Conn )
5	2 3 4	mp2an	⊢ ( ( topGen ‘ ran (,) ) ↾t ( 0 [,] 1 ) ) ∈ Conn
6	1 5	eqeltri	⊢ II ∈ Conn