Description: Transfinite Induction Schema, using implicit substitution. (Contributed by NM, 18-Aug-1994)
Ref | Expression | ||
---|---|---|---|
Hypotheses | tfis2.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
tfis2.2 | |- ( x e. On -> ( A. y e. x ps -> ph ) ) |
||
Assertion | tfis2 | |- ( x e. On -> ph ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | tfis2.1 | |- ( x = y -> ( ph <-> ps ) ) |
|
2 | tfis2.2 | |- ( x e. On -> ( A. y e. x ps -> ph ) ) |
|
3 | nfv | |- F/ x ps |
|
4 | 3 1 2 | tfis2f | |- ( x e. On -> ph ) |