Metamath Proof Explorer


Theorem bj-clex

Description: Sethood of certain classes. (Contributed by BJ, 2-Apr-2019)

Ref Expression
Assertion bj-clex
|- ( A e. V -> { x | { x } e. ( A " B ) } e. _V )

Proof

Step Hyp Ref Expression
1 imaexg
 |-  ( A e. V -> ( A " B ) e. _V )
2 bj-snsetex
 |-  ( ( A " B ) e. _V -> { x | { x } e. ( A " B ) } e. _V )
3 1 2 syl
 |-  ( A e. V -> { x | { x } e. ( A " B ) } e. _V )