Description: An equality inference for the maps-to notation. (Contributed by Mario Carneiro, 16-Dec-2013) (Proof shortened by SN, 11-Nov-2024)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | mpteq2ia.1 | |- ( x e. A -> B = C ) |
|
| Assertion | mpteq2ia | |- ( x e. A |-> B ) = ( x e. A |-> C ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | mpteq2ia.1 | |- ( x e. A -> B = C ) |
|
| 2 | 1 | adantl | |- ( ( T. /\ x e. A ) -> B = C ) |
| 3 | 2 | mpteq2dva | |- ( T. -> ( x e. A |-> B ) = ( x e. A |-> C ) ) |
| 4 | 3 | mptru | |- ( x e. A |-> B ) = ( x e. A |-> C ) |