Description: Slightly more general equality inference for the maps-to notation. (Contributed by Scott Fenton, 25-Apr-2012) Remove dependency on ax-10 . (Revised by SN, 11-Nov-2024)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | mpteq2dva.1 | |- ( ( ph /\ x e. A ) -> B = C ) |
|
| Assertion | mpteq2dva | |- ( ph -> ( x e. A |-> B ) = ( x e. A |-> C ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mpteq2dva.1 | |- ( ( ph /\ x e. A ) -> B = C ) |
|
| 2 | eqidd | |- ( ph -> A = A ) |
|
| 3 | 2 1 | mpteq12dva | |- ( ph -> ( x e. A |-> B ) = ( x e. A |-> C ) ) |