Metamath Proof Explorer


Theorem sseli

Description: Membership implication from subclass relationship. (Contributed by NM, 5-Aug-1993)

Ref Expression
Hypothesis sseli.1
|- A C_ B
Assertion sseli
|- ( C e. A -> C e. B )

Proof

Step Hyp Ref Expression
1 sseli.1
 |-  A C_ B
2 ssel
 |-  ( A C_ B -> ( C e. A -> C e. B ) )
3 1 2 ax-mp
 |-  ( C e. A -> C e. B )