Theorem compeq 38642

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

Assertion

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

Distinct variable group:   x, A

Proof of Theorem compeq

Step	Hyp	Ref	Expression
1		compel 38641	. 2 |- ( x e. ( _V \ A ) <-> -. x e. A )
2	1	abbi2i 2738	1 |- ( _V \ A ) = { x | -. x e. A }

Syntax hints:   -. wn 3   = wceq 1483   e. wcel 1990   {cab 2608   _Vcvv 3200   \ cdif 3571

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-5 1839  ax-6 1888  ax-7 1935  ax-9 1999  ax-10 2019  ax-11 2034  ax-12 2047  ax-13 2246  ax-ext 2602

This theorem depends on definitions:  df-bi 197  df-or 385  df-an 386  df-tru 1486  df-ex 1705  df-nf 1710  df-sb 1881  df-clab 2609  df-cleq 2615  df-clel 2618  df-nfc 2753  df-v 3202  df-dif 3577

This theorem is referenced by: (None)