Description: Version of cbvexdva with a disjoint variable condition, which does not require ax-13 . (Contributed by BJ, 16-Jun-2019) (Proof modification is discouraged.)
Ref | Expression | ||
---|---|---|---|
Hypothesis | bj-cbvaldvav.1 | |- ( ( ph /\ x = y ) -> ( ps <-> ch ) ) |
|
Assertion | bj-cbvexdvav | |- ( ph -> ( E. x ps <-> E. y ch ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | bj-cbvaldvav.1 | |- ( ( ph /\ x = y ) -> ( ps <-> ch ) ) |
|
2 | nfv | |- F/ y ph |
|
3 | nfvd | |- ( ph -> F/ y ps ) |
|
4 | 1 | ex | |- ( ph -> ( x = y -> ( ps <-> ch ) ) ) |
5 | 2 3 4 | bj-cbvexdv | |- ( ph -> ( E. x ps <-> E. y ch ) ) |