Description: A set is well-founded if all of its elements are well-founded. Proposition 9.12 of TakeutiZaring p. 78. The main proof consists of tz9.12lem1 through tz9.12lem3 . (Contributed by NM, 22-Sep-2003)
Ref | Expression | ||
---|---|---|---|
Hypothesis | tz9.12.1 | |
|
Assertion | tz9.12 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tz9.12.1 | |
|
2 | eqid | |
|
3 | 1 2 | tz9.12lem2 | |
4 | 3 | onsuci | |
5 | 1 2 | tz9.12lem3 | |
6 | fveq2 | |
|
7 | 6 | eleq2d | |
8 | 7 | rspcev | |
9 | 4 5 8 | sylancr | |