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Theorem dfdif2 3329
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
StepHypRef Expression
1 df-dif 3323 . 2  |-  ( A 
\  B )  =  { x  |  ( x  e.  A  /\  -.  x  e.  B
) }
2 df-rab 2714 . 2  |-  { x  e.  A  |  -.  x  e.  B }  =  { x  |  ( x  e.  A  /\  -.  x  e.  B
) }
31, 2eqtr4i 2459 1  |-  ( A 
\  B )  =  { x  e.  A  |  -.  x  e.  B }
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 359    = wceq 1652    e. wcel 1725   {cab 2422   {crab 2709    \ cdif 3317
This theorem is referenced by:  difeq1  3458  difeq2  3459  nfdif  3468  difidALT  3697  ordintdif  4630  kmlem3  8032  incexc2  12618  cnambfre  26255
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-11 1761  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-ex 1551  df-cleq 2429  df-rab 2714  df-dif 3323
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