Description: Obsolete version of sbc6g as of 5-Oct-2024. (Contributed by NM, 11-Oct-2004) (Proof shortened by Andrew Salmon, 8-Jun-2011) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | sbc6gOLD | |- ( A e. V -> ( [. A / x ]. ph <-> A. x ( x = A -> ph ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | sbc5 | |- ( [. A / x ]. ph <-> E. x ( x = A /\ ph ) ) |
|
| 2 | alexeqg | |- ( A e. V -> ( A. x ( x = A -> ph ) <-> E. x ( x = A /\ ph ) ) ) |
|
| 3 | 1 2 | bitr4id | |- ( A e. V -> ( [. A / x ]. ph <-> A. x ( x = A -> ph ) ) ) |