Description: Well-Ordered Induction schema, using implicit substitution. (Contributed by Scott Fenton, 29-Jan-2011)
Ref | Expression | ||
---|---|---|---|
Hypotheses | wfis2.1 | |- R We A |
|
wfis2.2 | |- R Se A |
||
wfis2.3 | |- ( y = z -> ( ph <-> ps ) ) |
||
wfis2.4 | |- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) ) |
||
Assertion | wfis2 | |- ( y e. A -> ph ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wfis2.1 | |- R We A |
|
2 | wfis2.2 | |- R Se A |
|
3 | wfis2.3 | |- ( y = z -> ( ph <-> ps ) ) |
|
4 | wfis2.4 | |- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) ) |
|
5 | 3 4 | wfis2g | |- ( ( R We A /\ R Se A ) -> A. y e. A ph ) |
6 | 1 2 5 | mp2an | |- A. y e. A ph |
7 | 6 | rspec | |- ( y e. A -> ph ) |