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Theorem inindir 3155
 Description: Intersection distributes over itself. (Contributed by NM, 17-Aug-2004.)
Assertion
Ref Expression
inindir

Proof of Theorem inindir
StepHypRef Expression
1 inidm 3146 . . 3
21ineq2i 3135 . 2
3 in4 3153 . 2
42, 3eqtr3i 2062 1
 Colors of variables: wff set class Syntax hints:   wceq 1243   cin 2916 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  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-nfc 2167  df-v 2559  df-in 2924 This theorem is referenced by:  difindir  3192  resindir  4628
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