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Theorem difeq2 3056
 Description: Equality theorem for class difference. (Contributed by NM, 10-Feb-1997.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
difeq2

Proof of Theorem difeq2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eleq2 2101 . . . 4
21notbid 592 . . 3
32rabbidv 2549 . 2
4 dfdif2 2926 . 2
5 dfdif2 2926 . 2
63, 4, 53eqtr4g 2097 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1243   wcel 1393  crab 2310   cdif 2914 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-in1 544  ax-in2 545  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-ral 2311  df-rab 2315  df-dif 2920 This theorem is referenced by:  difeq12  3057  difeq2i  3059  difeq2d  3062  ssdifeq0  3305  2oconcl  6022  diffitest  6344  diffifi  6351
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