Theorem dfdif2 2059

Description: Alternate definition of class difference.

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 2052	. 2 |- (A \ B) = {x | (x e. A /\ -. x e. B)}
2		df-rab 1655	. 2 |- {x e. A | -. x e. B} = {x | (x e. A /\ -. x e. B)}
3	1, 2	eqtr4 1501	1 |- (A \ B) = {x e. A | -. x e. B}

Syntax hints:  -. wn 2   /\ wa 223   = wceq 958   e. wcel 960  {cab 1466  {crab 1651   \ cdif 2047

This theorem is referenced by:  kmlem3 4777

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-gen 965  ax-17 973  ax-4 975  ax-5o 977  ax-ext 1462

This theorem depends on definitions:  df-bi 147  df-an 225  df-cleq 1472  df-rab 1655  df-dif 2052

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