Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | bnj118.1 | |- ( ph <-> ( f ` (/) ) = _pred ( x , A , R ) ) |
|
bnj118.2 | |- ( ph' <-> [. 1o / n ]. ph ) |
||
Assertion | bnj118 | |- ( ph' <-> ( f ` (/) ) = _pred ( x , A , R ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bnj118.1 | |- ( ph <-> ( f ` (/) ) = _pred ( x , A , R ) ) |
|
2 | bnj118.2 | |- ( ph' <-> [. 1o / n ]. ph ) |
|
3 | bnj105 | |- 1o e. _V |
|
4 | 1 3 | bnj91 | |- ( [. 1o / n ]. ph <-> ( f ` (/) ) = _pred ( x , A , R ) ) |
5 | 2 4 | bitri | |- ( ph' <-> ( f ` (/) ) = _pred ( x , A , R ) ) |