Description: Technical lemma for bnj852 . 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 | ||
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Hypotheses | bnj523.1 | |- ( ph <-> ( F ` (/) ) = _pred ( X , A , R ) ) |
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bnj523.2 | |- ( ph' <-> [. M / n ]. ph ) |
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bnj523.3 | |- M e. _V |
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Assertion | bnj523 | |- ( ph' <-> ( F ` (/) ) = _pred ( X , A , R ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj523.1 | |- ( ph <-> ( F ` (/) ) = _pred ( X , A , R ) ) |
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2 | bnj523.2 | |- ( ph' <-> [. M / n ]. ph ) |
|
3 | bnj523.3 | |- M e. _V |
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4 | 1 | sbcbii | |- ( [. M / n ]. ph <-> [. M / n ]. ( F ` (/) ) = _pred ( X , A , R ) ) |
5 | 3 | bnj525 | |- ( [. M / n ]. ( F ` (/) ) = _pred ( X , A , R ) <-> ( F ` (/) ) = _pred ( X , A , R ) ) |
6 | 2 4 5 | 3bitri | |- ( ph' <-> ( F ` (/) ) = _pred ( X , A , R ) ) |