Description: Equality implies equivalence of membership. (Contributed by NM, 26-May-1993) (Proof shortened by Wolf Lammen, 20-Nov-2019)
Ref | Expression | ||
---|---|---|---|
Assertion | eleq2 | |- ( A = B -> ( C e. A <-> C e. B ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id | |- ( A = B -> A = B ) |
|
2 | 1 | eleq2d | |- ( A = B -> ( C e. A <-> C e. B ) ) |