Description: Technical lemma for bnj150 . 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 | bnj126.1 | |- ( ps <-> A. i e. _om ( suc i e. n -> ( f ` suc i ) = U_ y e. ( f ` i ) _pred ( y , A , R ) ) ) |
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| bnj126.2 | |- ( ps' <-> [. 1o / n ]. ps ) |
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| bnj126.3 | |- ( ps" <-> [. F / f ]. ps' ) |
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| bnj126.4 | |- F = { <. (/) , _pred ( x , A , R ) >. } |
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| Assertion | bnj126 | |- ( ps" <-> A. i e. _om ( suc i e. 1o -> ( F ` suc i ) = U_ y e. ( F ` i ) _pred ( y , A , R ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | bnj126.1 | |- ( ps <-> A. i e. _om ( suc i e. n -> ( f ` suc i ) = U_ y e. ( f ` i ) _pred ( y , A , R ) ) ) |
|
| 2 | bnj126.2 | |- ( ps' <-> [. 1o / n ]. ps ) |
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| 3 | bnj126.3 | |- ( ps" <-> [. F / f ]. ps' ) |
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| 4 | bnj126.4 | |- F = { <. (/) , _pred ( x , A , R ) >. } |
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| 5 | 2 | sbcbii | |- ( [. F / f ]. ps' <-> [. F / f ]. [. 1o / n ]. ps ) |
| 6 | 4 | bnj95 | |- F e. _V |
| 7 | 1 6 | bnj106 | |- ( [. F / f ]. [. 1o / n ]. ps <-> A. i e. _om ( suc i e. 1o -> ( F ` suc i ) = U_ y e. ( F ` i ) _pred ( y , A , R ) ) ) |
| 8 | 3 5 7 | 3bitri | |- ( ps" <-> A. i e. _om ( suc i e. 1o -> ( F ` suc i ) = U_ y e. ( F ` i ) _pred ( y , A , R ) ) ) |