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Theorem invdif 3324
 Description: Intersection with universal complement. Remark in [Stoll] p. 20. (Contributed by NM, 17-Aug-2004.)
Assertion
Ref Expression
invdif

Proof of Theorem invdif
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 vex 2693 . . . . 5
2 eldif 3086 . . . . 5
31, 2mpbiran 925 . . . 4
43anbi2i 453 . . 3
5 elin 3265 . . 3
6 eldif 3086 . . 3
74, 5, 63bitr4i 211 . 2
87eqriv 2137 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 103   wceq 1332   wcel 1481  cvv 2690   cdif 3074   cin 3076 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-in1 604  ax-in2 605  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-dif 3079  df-in 3083 This theorem is referenced by:  indif2  3326  difundir  3335  difindir  3337  difdif2ss  3339  difun1  3342  difdifdirss  3453  nn0supp  9073
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