Description: Version of 19.42 with two quantifiers and a disjoint variable condition requiring fewer axioms. (Contributed by NM, 16-Mar-1995)
Ref | Expression | ||
---|---|---|---|
Assertion | 19.42vv | |- ( E. x E. y ( ph /\ ps ) <-> ( ph /\ E. x E. y ps ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exdistr | |- ( E. x E. y ( ph /\ ps ) <-> E. x ( ph /\ E. y ps ) ) |
|
2 | 19.42v | |- ( E. x ( ph /\ E. y ps ) <-> ( ph /\ E. x E. y ps ) ) |
|
3 | 1 2 | bitri | |- ( E. x E. y ( ph /\ ps ) <-> ( ph /\ E. x E. y ps ) ) |