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Theorem difeq1 3194
 Description: Equality theorem for class difference. (Contributed by NM, 10-Feb-1997.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Assertion
Ref Expression
difeq1

Proof of Theorem difeq1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 rabeq 2683 . 2
2 dfdif2 3086 . 2
3 dfdif2 3086 . 2
41, 2, 33eqtr4g 2199 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wceq 1332   wcel 2112  crab 2422   cdif 3075 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-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-ext 2123 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1732  df-clab 2128  df-cleq 2134  df-clel 2137  df-nfc 2272  df-rab 2427  df-dif 3080 This theorem is referenced by:  difeq12  3196  difeq1i  3197  difeq1d  3200  uneqdifeqim  3455  diffitest  6793
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