Description: A subset of the nonnegative integers defined by a restricted class abstraction is finite if there is a nonnegative integer so that for all integers greater than this integer the condition of the class abstraction is not fulfilled. (Contributed by AV, 3-Oct-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | rabssnn0fi | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssrab2 | |
|
2 | ssnn0fi | |
|
3 | nnel | |
|
4 | nfcv | |
|
5 | nfcv | |
|
6 | nfsbc1v | |
|
7 | 6 | nfn | |
8 | sbceq2a | |
|
9 | 8 | equcoms | |
10 | 9 | con2bid | |
11 | 4 5 7 10 | elrabf | |
12 | 11 | baib | |
13 | 3 12 | syl5bb | |
14 | 13 | con4bid | |
15 | 14 | imbi2d | |
16 | 15 | ralbiia | |
17 | nfv | |
|
18 | 17 6 | nfim | |
19 | nfv | |
|
20 | breq2 | |
|
21 | 20 8 | imbi12d | |
22 | 18 19 21 | cbvralw | |
23 | 16 22 | bitri | |
24 | 23 | a1i | |
25 | 24 | rexbidva | |
26 | 2 25 | bitrd | |
27 | 1 26 | ax-mp | |