Description: An equivalence for class substitution. (Contributed by NM, 11-Oct-2004) (Proof shortened by Andrew Salmon, 8-Jun-2011) (Proof shortened by SN, 5-Oct-2024)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | sbc6g | |- ( A e. V -> ( [. A / x ]. ph <-> A. x ( x = A -> ph ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-sbc | |- ( [. A / x ]. ph <-> A e. { x | ph } ) |
|
| 2 | elab6g | |- ( A e. V -> ( A e. { x | ph } <-> A. x ( x = A -> ph ) ) ) |
|
| 3 | 1 2 | syl5bb | |- ( A e. V -> ( [. A / x ]. ph <-> A. x ( x = A -> ph ) ) ) |