Description: A function with bounded domain and range is a set. This version of fex is proven without the Axiom of Replacement. (Contributed by Mario Carneiro, 24-Jun-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | fex2 | |- ( ( F : A --> B /\ A e. V /\ B e. W ) -> F e. _V ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpexg | |- ( ( A e. V /\ B e. W ) -> ( A X. B ) e. _V ) |
|
2 | 1 | 3adant1 | |- ( ( F : A --> B /\ A e. V /\ B e. W ) -> ( A X. B ) e. _V ) |
3 | fssxp | |- ( F : A --> B -> F C_ ( A X. B ) ) |
|
4 | 3 | 3ad2ant1 | |- ( ( F : A --> B /\ A e. V /\ B e. W ) -> F C_ ( A X. B ) ) |
5 | 2 4 | ssexd | |- ( ( F : A --> B /\ A e. V /\ B e. W ) -> F e. _V ) |