Description: Version of bj-vtoclg1f with a disjoint variable condition on x , V . This removes dependency on df-sb and df-clab . Prefer its use over bj-vtoclg1f when sufficient (in particular when V is substituted for _V ). (Contributed by BJ, 14-Sep-2019) (Proof modification is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypotheses | bj-vtoclg1fv.nf | |- F/ x ps |
|
bj-vtoclg1fv.maj | |- ( x = A -> ( ph -> ps ) ) |
||
bj-vtoclg1fv.min | |- ph |
||
Assertion | bj-vtoclg1fv | |- ( A e. V -> ps ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-vtoclg1fv.nf | |- F/ x ps |
|
2 | bj-vtoclg1fv.maj | |- ( x = A -> ( ph -> ps ) ) |
|
3 | bj-vtoclg1fv.min | |- ph |
|
4 | elissetv | |- ( A e. V -> E. x x = A ) |
|
5 | 1 2 3 | bj-exlimmpi | |- ( E. x x = A -> ps ) |
6 | 4 5 | syl | |- ( A e. V -> ps ) |