Metamath Proof Explorer

Theorem ssnel

Description: If not element of a set, then not element of a subset. (Contributed by Glauco Siliprandi, 11-Dec-2019)

Ref Expression
Assertion ssnel 
|- ( ( A C_ B /\ -. C e. B ) -> -. C e. A )

Proof

Step Hyp Ref Expression
1 ssel2 
 |-  ( ( A C_ B /\ C e. A ) -> C e. B )
2 1 stoic1a 
 |-  ( ( A C_ B /\ -. C e. B ) -> -. C e. A )