Metamath Proof Explorer


Theorem fsetcdmex

Description: The class of all functions from a nonempty set A into a class B is a set iff B is a set . (Contributed by AV, 15-Sep-2024)

Ref Expression
Assertion fsetcdmex A V A B V f | f : A B V

Proof

Step Hyp Ref Expression
1 fsetex B V f | f : A B V
2 fsetprcnex A V A B V f | f : A B V
3 2 ex A V A B V f | f : A B V
4 df-nel B V ¬ B V
5 df-nel f | f : A B V ¬ f | f : A B V
6 3 4 5 3imtr3g A V A ¬ B V ¬ f | f : A B V
7 6 con4d A V A f | f : A B V B V
8 1 7 impbid2 A V A B V f | f : A B V