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Theorem dfdif2 3398
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 3392 . 2  |-  ( A 
\  B )  =  { x  |  ( x  e.  A  /\  -.  x  e.  B
) }
2 df-rab 2741 . 2  |-  { x  e.  A  |  -.  x  e.  B }  =  { x  |  ( x  e.  A  /\  -.  x  e.  B
) }
31, 2eqtr4i 2414 1  |-  ( A 
\  B )  =  { x  e.  A  |  -.  x  e.  B }
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    /\ wa 367    = wceq 1399    e. wcel 1826   {cab 2367   {crab 2736    \ cdif 3386
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1626  ax-4 1639  ax-ext 2360
This theorem depends on definitions:  df-bi 185  df-cleq 2374  df-rab 2741  df-dif 3392
This theorem is referenced by:  difeq1  3529  difeq2  3530  nfdif  3539  difidALT  3813  ordintdif  4841  kmlem3  8445  incexc2  13652  cnambfre  30228
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