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Theorem dfdif2 2920
Description: Alternate definition of class difference. (Contributed by NM, 25-Mar-2004.)
Assertion
Ref Expression
dfdif2 (AB) = {x A ∣ ¬ x B}
Distinct variable groups:   x,A   x,B

Proof of Theorem dfdif2
StepHypRef Expression
1 df-dif 2914 . 2 (AB) = {x ∣ (x A ¬ x B)}
2 df-rab 2309 . 2 {x A ∣ ¬ x B} = {x ∣ (x A ¬ x B)}
31, 2eqtr4i 2060 1 (AB) = {x A ∣ ¬ x B}
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   wa 97   = wceq 1242   wcel 1390  {cab 2023  {crab 2304  cdif 2908
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-4 1397  ax-17 1416  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-cleq 2030  df-rab 2309  df-dif 2914
This theorem is referenced by:  difeq1  3049  difeq2  3050  nfdif  3059  difidALT  3287
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