Description: Obsolete version of sb3b as of 21-Feb-2024. (Contributed by BJ, 6-Oct-2018) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | sb3bOLD | |- ( -. A. x x = y -> ( [ y / x ] ph <-> E. x ( x = y /\ ph ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sb1 | |- ( [ y / x ] ph -> E. x ( x = y /\ ph ) ) |
|
| 2 | sb3 | |- ( -. A. x x = y -> ( E. x ( x = y /\ ph ) -> [ y / x ] ph ) ) |
|
| 3 | 1 2 | impbid2 | |- ( -. A. x x = y -> ( [ y / x ] ph <-> E. x ( x = y /\ ph ) ) ) |