Description: Remove from ceqsal dependency on ax-ext (and on df-cleq , df-v , df-clab , df-sb ). (Contributed by BJ, 12-Oct-2019) (Proof modification is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | bj-ceqsal.1 | |- F/ x ps |
|
bj-ceqsal.2 | |- A e. _V |
||
bj-ceqsal.3 | |- ( x = A -> ( ph <-> ps ) ) |
||
Assertion | bj-ceqsal | |- ( A. x ( x = A -> ph ) <-> ps ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-ceqsal.1 | |- F/ x ps |
|
2 | bj-ceqsal.2 | |- A e. _V |
|
3 | bj-ceqsal.3 | |- ( x = A -> ( ph <-> ps ) ) |
|
4 | 1 3 | bj-ceqsalgv | |- ( A e. _V -> ( A. x ( x = A -> ph ) <-> ps ) ) |
5 | 2 4 | ax-mp | |- ( A. x ( x = A -> ph ) <-> ps ) |