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Theorem resindir 4742
 Description: Class restriction distributes over intersection. (Contributed by NM, 18-Dec-2008.)
Assertion
Ref Expression
resindir

Proof of Theorem resindir
StepHypRef Expression
1 inindir 3219 . 2
2 df-res 4464 . 2
3 df-res 4464 . . 3
4 df-res 4464 . . 3
53, 4ineq12i 3200 . 2
61, 2, 53eqtr4i 2119 1
 Colors of variables: wff set class Syntax hints:   wceq 1290  cvv 2620   cin 2999   cxp 4450   cres 4454 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071 This theorem depends on definitions:  df-bi 116  df-tru 1293  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2622  df-in 3006  df-res 4464 This theorem is referenced by:  inimass  4861  fnreseql  5423
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