Description: Property of a III-finite set (descending sequence version). (Contributed by Mario Carneiro, 16-May-2015)
Ref | Expression | ||
---|---|---|---|
Hypothesis | isfin3ds.f | |
|
Assertion | isfin3ds | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isfin3ds.f | |
|
2 | suceq | |
|
3 | 2 | fveq2d | |
4 | fveq2 | |
|
5 | 3 4 | sseq12d | |
6 | 5 | cbvralvw | |
7 | fveq1 | |
|
8 | fveq1 | |
|
9 | 7 8 | sseq12d | |
10 | 9 | ralbidv | |
11 | 6 10 | syl5bb | |
12 | rneq | |
|
13 | 12 | inteqd | |
14 | 13 12 | eleq12d | |
15 | 11 14 | imbi12d | |
16 | 15 | cbvralvw | |
17 | pweq | |
|
18 | 17 | oveq1d | |
19 | 18 | raleqdv | |
20 | 16 19 | syl5bb | |
21 | 20 1 | elab2g | |