Theorem dfdif2 3228

Description: Alternate definition of class difference. (Contributed by NM, 25-Mar-2004.)

Assertion

Ref	Expression
dfdif2	|- ( A \ B ) = { x e. A | -. x e. B }

Distinct variable groups:   x, A   x, B

Proof of Theorem dfdif2

Step	Hyp	Ref	Expression
1		df-dif 3222	. 2 |- ( A \ B ) = { x | ( x e. A /\ -. x e. B ) }
2		df-rab 2537	. 2 |- { x e. A | -. x e. B } = { x | ( x e. A /\ -. x e. B ) }
3	1, 2	eqtr4i 2262	1 |- ( A \ B ) = { x e. A | -. x e. B }

Syntax hints:   -. wn 3   /\ wa 104   = wceq 1402   e. wcel 2209   {cab 2224   {crab 2532   \ cdif 3217

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-4 1563  ax-17 1579  ax-ext 2220

This theorem depends on definitions:  df-bi 117  df-cleq 2231  df-rab 2537  df-dif 3222

This theorem is referenced by:  dfdif3  3339  difeq1  3340  difeq2  3341  nfdif  3350  difidALT  3593