Description: An equivalence related to implicit substitution. Usage of this theorem is discouraged because it depends on ax-13 . See equsexhv for a version with a disjoint variable condition which does not require ax-13 . (Contributed by NM, 5-Aug-1993) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | equsalh.1 | |- ( ps -> A. x ps ) |
|
| equsalh.2 | |- ( x = y -> ( ph <-> ps ) ) |
||
| Assertion | equsexh | |- ( E. x ( x = y /\ ph ) <-> ps ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | equsalh.1 | |- ( ps -> A. x ps ) |
|
| 2 | equsalh.2 | |- ( x = y -> ( ph <-> ps ) ) |
|
| 3 | 1 | nf5i | |- F/ x ps |
| 4 | 3 2 | equsex | |- ( E. x ( x = y /\ ph ) <-> ps ) |