Metamath Proof Explorer


Theorem elqsi

Description: Membership in a quotient set. (Contributed by NM, 23-Jul-1995)

Ref Expression
Assertion elqsi
|- ( B e. ( A /. R ) -> E. x e. A B = [ x ] R )

Proof

Step Hyp Ref Expression
1 elqsg
 |-  ( B e. ( A /. R ) -> ( B e. ( A /. R ) <-> E. x e. A B = [ x ] R ) )
2 1 ibi
 |-  ( B e. ( A /. R ) -> E. x e. A B = [ x ] R )