Description: Technical lemma for bnj69 . This lemma may no longer be used or have become an indirect lemma of the theorem in question (i.e. a lemma of a lemma... of the theorem). (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | bnj1039.1 | |- ( ps <-> A. i e. _om ( suc i e. n -> ( f ` suc i ) = U_ y e. ( f ` i ) _pred ( y , A , R ) ) ) |
|
| bnj1039.2 | |- ( ps' <-> [. j / i ]. ps ) |
||
| Assertion | bnj1039 | |- ( ps' <-> A. i e. _om ( suc i e. n -> ( f ` suc i ) = U_ y e. ( f ` i ) _pred ( y , A , R ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bnj1039.1 | |- ( ps <-> A. i e. _om ( suc i e. n -> ( f ` suc i ) = U_ y e. ( f ` i ) _pred ( y , A , R ) ) ) |
|
| 2 | bnj1039.2 | |- ( ps' <-> [. j / i ]. ps ) |
|
| 3 | vex | |- j e. _V |
|
| 4 | nfra1 | |- F/ i A. i e. _om ( suc i e. n -> ( f ` suc i ) = U_ y e. ( f ` i ) _pred ( y , A , R ) ) |
|
| 5 | 1 4 | nfxfr | |- F/ i ps |
| 6 | 3 5 | sbcgfi | |- ( [. j / i ]. ps <-> ps ) |
| 7 | 2 6 1 | 3bitri | |- ( ps' <-> A. i e. _om ( suc i e. n -> ( f ` suc i ) = U_ y e. ( f ` i ) _pred ( y , A , R ) ) ) |