Description: The real numbers are locally simply connected. (Contributed by Mario Carneiro, 10-Mar-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | rellysconn | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | retop | |
|
2 | tg2 | |
|
3 | retopbas | |
|
4 | bastg | |
|
5 | 3 4 | ax-mp | |
6 | simprl | |
|
7 | 5 6 | sselid | |
8 | simprrr | |
|
9 | velpw | |
|
10 | 8 9 | sylibr | |
11 | 7 10 | elind | |
12 | simprrl | |
|
13 | ioof | |
|
14 | ffn | |
|
15 | ovelrn | |
|
16 | 13 14 15 | mp2b | |
17 | oveq2 | |
|
18 | ioosconn | |
|
19 | 17 18 | eqeltrdi | |
20 | 19 | rexlimivw | |
21 | 20 | rexlimivw | |
22 | 16 21 | sylbi | |
23 | 22 | ad2antrl | |
24 | 11 12 23 | jca32 | |
25 | 24 | ex | |
26 | 25 | reximdv2 | |
27 | 2 26 | mpd | |
28 | 27 | rgen2 | |
29 | islly | |
|
30 | 1 28 29 | mpbir2an | |