Description: Alternate proof of dmfex : shorter but using ax-rep . (Contributed by NM, 27-Aug-2006) (Proof shortened by Andrew Salmon, 17-Sep-2011) (Proof shortened by AV, 23-Aug-2024) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | dmfexALT | |- ( ( F e. C /\ F : A --> B ) -> A e. _V ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elex | |- ( F e. C -> F e. _V ) |
|
| 2 | fdmexb | |- ( F : A --> B -> ( A e. _V <-> F e. _V ) ) |
|
| 3 | 2 | biimprd | |- ( F : A --> B -> ( F e. _V -> A e. _V ) ) |
| 4 | 1 3 | mpan9 | |- ( ( F e. C /\ F : A --> B ) -> A e. _V ) |