Description: The at-most-one quantifier reverses implication. (Contributed by NM, 15-Feb-2006) Remove use of ax-5 . (Revised by Steven Nguyen, 9-May-2023)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | moimi.1 | |- ( ph -> ps ) |
|
| Assertion | moimi | |- ( E* x ps -> E* x ph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | moimi.1 | |- ( ph -> ps ) |
|
| 2 | 1 | imim1i | |- ( ( ps -> x = y ) -> ( ph -> x = y ) ) |
| 3 | 2 | alimi | |- ( A. x ( ps -> x = y ) -> A. x ( ph -> x = y ) ) |
| 4 | 3 | eximi | |- ( E. y A. x ( ps -> x = y ) -> E. y A. x ( ph -> x = y ) ) |
| 5 | df-mo | |- ( E* x ps <-> E. y A. x ( ps -> x = y ) ) |
|
| 6 | df-mo | |- ( E* x ph <-> E. y A. x ( ph -> x = y ) ) |
|
| 7 | 4 5 6 | 3imtr4i | |- ( E* x ps -> E* x ph ) |