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Theorem dfdif2 3421
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 3415 . 2  |-  ( A 
\  B )  =  { x  |  ( x  e.  A  /\  -.  x  e.  B
) }
2 df-rab 2801 . 2  |-  { x  e.  A  |  -.  x  e.  B }  =  { x  |  ( x  e.  A  /\  -.  x  e.  B
) }
31, 2eqtr4i 2481 1  |-  ( A 
\  B )  =  { x  e.  A  |  -.  x  e.  B }
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    /\ wa 369    = wceq 1370    e. wcel 1757   {cab 2435   {crab 2796    \ cdif 3409
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-5 1671  ax-6 1709  ax-7 1729  ax-12 1793  ax-ext 2429
This theorem depends on definitions:  df-bi 185  df-ex 1588  df-cleq 2442  df-rab 2801  df-dif 3415
This theorem is referenced by:  difeq1  3551  difeq2  3552  nfdif  3561  difidALT  3832  ordintdif  4852  kmlem3  8408  incexc2  13389  cnambfre  28564
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