Metamath Proof Explorer

Theorem ecexg

Description: An equivalence class modulo a set is a set. (Contributed by NM, 24-Jul-1995)

Ref Expression
Assertion ecexg 
|- ( R e. B -> [ A ] R e. _V )

Proof

Step Hyp Ref Expression
1 df-ec 
 |-  [ A ] R = ( R " { A } )
2 imaexg 
 |-  ( R e. B -> ( R " { A } ) e. _V )
3 1 2 eqeltrid 
 |-  ( R e. B -> [ A ] R e. _V )