Description: Value of the cumulative hierarchy of sets function at a limit ordinal. Part of Definition 9.9 of TakeutiZaring p. 76. (Contributed by Mario Carneiro, 16-Nov-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | r1limg | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-r1 | |
|
2 | 1 | dmeqi | |
3 | 2 | eleq2i | |
4 | rdglimg | |
|
5 | 3 4 | sylanb | |
6 | 1 | fveq1i | |
7 | r1funlim | |
|
8 | 7 | simpli | |
9 | funiunfv | |
|
10 | 8 9 | ax-mp | |
11 | 1 | imaeq1i | |
12 | 11 | unieqi | |
13 | 10 12 | eqtri | |
14 | 5 6 13 | 3eqtr4g | |