Description: Well-Ordered Induction Schema, using implicit substitution. (Contributed by Scott Fenton, 11-Feb-2011)
Ref | Expression | ||
---|---|---|---|
Hypotheses | wfis2g.1 | |- ( y = z -> ( ph <-> ps ) ) |
|
wfis2g.2 | |- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) ) |
||
Assertion | wfis2g | |- ( ( R We A /\ R Se A ) -> A. y e. A ph ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wfis2g.1 | |- ( y = z -> ( ph <-> ps ) ) |
|
2 | wfis2g.2 | |- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) ) |
|
3 | nfv | |- F/ y ps |
|
4 | 3 1 2 | wfis2fg | |- ( ( R We A /\ R Se A ) -> A. y e. A ph ) |