Metamath Proof Explorer

Theorem compeq

Description: Equality between two ways of saying "the complement of A ". (Contributed by Andrew Salmon, 15-Jul-2011)

Ref Expression
Assertion compeq 
|- ( _V \ A ) = { x | -. x e. A }

Proof

Step Hyp Ref Expression
1 velcomp 
 |-  ( x e. ( _V \ A ) <-> -. x e. A )
2 1 eqabi 
 |-  ( _V \ A ) = { x | -. x e. A }