Metamath Proof Explorer

Theorem ecelqsi

Description: Membership of an equivalence class in a quotient set. (Contributed by NM, 25-Jul-1995) (Revised by Mario Carneiro, 9-Jul-2014)

Ref Expression
Hypothesis ecelqsi.1 
|- R e. _V
Assertion ecelqsi 
|- ( B e. A -> [ B ] R e. ( A /. R ) )

Proof

Step Hyp Ref Expression
1 ecelqsi.1 
 |-  R e. _V
2 ecelqsg 
 |-  ( ( R e. _V /\ B e. A ) -> [ B ] R e. ( A /. R ) )
3 1 2 mpan 
 |-  ( B e. A -> [ B ] R e. ( A /. R ) )