Description: Well-Founded Induction schema, using implicit substitution. (Contributed by Scott Fenton, 24-Aug-2022)
Ref | Expression | ||
---|---|---|---|
Hypotheses | frpoins2g.1 | |- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) ) |
|
frpoins2g.3 | |- ( y = z -> ( ph <-> ps ) ) |
||
Assertion | frpoins2g | |- ( ( R Fr A /\ R Po A /\ R Se A ) -> A. y e. A ph ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | frpoins2g.1 | |- ( y e. A -> ( A. z e. Pred ( R , A , y ) ps -> ph ) ) |
|
2 | frpoins2g.3 | |- ( y = z -> ( ph <-> ps ) ) |
|
3 | nfv | |- F/ y ps |
|
4 | 1 3 2 | frpoins2fg | |- ( ( R Fr A /\ R Po A /\ R Se A ) -> A. y e. A ph ) |