Description: Obsolete version of sbalex as of 14-Aug-2025. (Contributed by NM, 14-Apr-2008) (Revised by BJ, 20-Dec-2020) (Revised by BJ, 21-Sep-2024) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | sbalexOLD | |- ( E. x ( x = t /\ ph ) <-> A. x ( x = t -> ph ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nfa1 | |- F/ x A. x ( x = t -> ph ) |
|
| 2 | ax12v2 | |- ( x = t -> ( ph -> A. x ( x = t -> ph ) ) ) |
|
| 3 | 2 | imp | |- ( ( x = t /\ ph ) -> A. x ( x = t -> ph ) ) |
| 4 | 1 3 | exlimi | |- ( E. x ( x = t /\ ph ) -> A. x ( x = t -> ph ) ) |
| 5 | equs4v | |- ( A. x ( x = t -> ph ) -> E. x ( x = t /\ ph ) ) |
|
| 6 | 4 5 | impbii | |- ( E. x ( x = t /\ ph ) <-> A. x ( x = t -> ph ) ) |