Description: An equivalence for class substitution. (Contributed by NM, 11-Oct-2004) (Proof shortened by Andrew Salmon, 8-Jun-2011)
Ref | Expression | ||
---|---|---|---|
Assertion | sbc6g | |- ( 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 ) ) ) |