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Theorem indif1 3242
 Description: Bring an intersection in and out of a class difference. (Contributed by Mario Carneiro, 15-May-2015.)
Assertion
Ref Expression
indif1

Proof of Theorem indif1
StepHypRef Expression
1 indif2 3241 . 2
2 incom 3190 . 2
3 incom 3190 . . 3
43difeq1i 3112 . 2
51, 2, 43eqtr3i 2116 1
 Colors of variables: wff set class Syntax hints:   wceq 1289   cdif 2994   cin 2996 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070 This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-rab 2368  df-v 2621  df-dif 2999  df-in 3003 This theorem is referenced by:  resdmdfsn  4742
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