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Theorem dfdif2 3110
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 3104 . 2  |-  ( A 
\  B )  =  { x  |  ( x  e.  A  /\  -.  x  e.  B
) }
2 df-rab 2444 . 2  |-  { x  e.  A  |  -.  x  e.  B }  =  { x  |  ( x  e.  A  /\  -.  x  e.  B
) }
31, 2eqtr4i 2181 1  |-  ( A 
\  B )  =  { x  e.  A  |  -.  x  e.  B }
Colors of variables: wff set class
Syntax hints:   -. wn 3    /\ wa 103    = wceq 1335    e. wcel 2128   {cab 2143   {crab 2439    \ cdif 3099
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1427  ax-gen 1429  ax-4 1490  ax-17 1506  ax-ext 2139
This theorem depends on definitions:  df-bi 116  df-cleq 2150  df-rab 2444  df-dif 3104
This theorem is referenced by:  dfdif3  3217  difeq1  3218  difeq2  3219  nfdif  3228  difidALT  3463
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