Description: Remove from ceqsalg dependency on ax-ext (and on df-cleq and df-v ). See also bj-ceqsalgv . (Contributed by BJ, 12-Oct-2019) (Proof modification is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | bj-ceqsalg.1 | |- F/ x ps |
|
bj-ceqsalg.2 | |- ( x = A -> ( ph <-> ps ) ) |
||
Assertion | bj-ceqsalg | |- ( A e. V -> ( A. x ( x = A -> ph ) <-> ps ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-ceqsalg.1 | |- F/ x ps |
|
2 | bj-ceqsalg.2 | |- ( x = A -> ( ph <-> ps ) ) |
|
3 | bj-elisset | |- ( A e. V -> E. x x = A ) |
|
4 | 1 2 | bj-ceqsalg0 | |- ( E. x x = A -> ( A. x ( x = A -> ph ) <-> ps ) ) |
5 | 3 4 | syl | |- ( A e. V -> ( A. x ( x = A -> ph ) <-> ps ) ) |