This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem ssel2

Description: Membership relationships follow from a subclass relationship. (Contributed by NM, 7-Jun-2004)

Ref Expression
Assertion ssel2 
|- ( ( A C_ B /\ C e. A ) -> C e. B )

Proof

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