Description: Equality theorem for ordinal isomorphism. (Contributed by Mario Carneiro, 23-May-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | oieq2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | weeq2 | |
|
2 | seeq2 | |
|
3 | 1 2 | anbi12d | |
4 | rabeq | |
|
5 | 4 | raleqdv | |
6 | 4 5 | riotaeqbidv | |
7 | 6 | mpteq2dv | |
8 | recseq | |
|
9 | 7 8 | syl | |
10 | 9 | imaeq1d | |
11 | 10 | raleqdv | |
12 | 11 | rexeqbi1dv | |
13 | 12 | rabbidv | |
14 | 9 13 | reseq12d | |
15 | 3 14 | ifbieq1d | |
16 | df-oi | |
|
17 | df-oi | |
|
18 | 15 16 17 | 3eqtr4g | |