Metamath Proof Explorer

Theorem prcssprc

Description: The superclass of a proper class is a proper class. (Contributed by AV, 27-Dec-2020)

Ref Expression
Assertion prcssprc 
|- ( ( A C_ B /\ A e/ _V ) -> B e/ _V )

Proof

Step Hyp Ref Expression
1 ssexg 
 |-  ( ( A C_ B /\ B e. _V ) -> A e. _V )
2 1 ex 
 |-  ( A C_ B -> ( B e. _V -> A e. _V ) )
3 2 nelcon3d 
 |-  ( A C_ B -> ( A e/ _V -> B e/ _V ) )
4 3 imp 
 |-  ( ( A C_ B /\ A e/ _V ) -> B e/ _V )