Description: Condition for a class abstraction to be a singleton. Formerly part of proof of dfiota2 . (Contributed by Andrew Salmon, 30-Jun-2011) (Revised by AV, 24-Aug-2022)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | absn | |- ( { x | ph } = { Y } <-> A. x ( ph <-> x = Y ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-sn | |- { Y } = { x | x = Y } |
|
| 2 | 1 | eqeq2i | |- ( { x | ph } = { Y } <-> { x | ph } = { x | x = Y } ) |
| 3 | abbi | |- ( A. x ( ph <-> x = Y ) <-> { x | ph } = { x | x = Y } ) |
|
| 4 | 2 3 | bitr4i | |- ( { x | ph } = { Y } <-> A. x ( ph <-> x = Y ) ) |