Description: Nonemptiness of an initial segment in terms of range. (Contributed by Stefan O'Rear, 18-Jan-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | inisegn0 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elex | |
|
2 | snprc | |
|
3 | 2 | biimpi | |
4 | 3 | imaeq2d | |
5 | ima0 | |
|
6 | 4 5 | eqtrdi | |
7 | 6 | necon1ai | |
8 | eleq1 | |
|
9 | sneq | |
|
10 | 9 | imaeq2d | |
11 | 10 | neeq1d | |
12 | abn0 | |
|
13 | iniseg | |
|
14 | 13 | elv | |
15 | 14 | neeq1i | |
16 | vex | |
|
17 | 16 | elrn | |
18 | 12 15 17 | 3bitr4ri | |
19 | 8 11 18 | vtoclbg | |
20 | 1 7 19 | pm5.21nii | |