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Theorem resindi 5294
 Description: Class restriction distributes over intersection. (Contributed by FL, 6-Oct-2008.)
Assertion
Ref Expression
resindi

Proof of Theorem resindi
StepHypRef Expression
1 xpindir 5142 . . . 4
21ineq2i 3696 . . 3
3 inindi 3714 . . 3
42, 3eqtri 2486 . 2
5 df-res 5016 . 2
6 df-res 5016 . . 3
7 df-res 5016 . . 3
86, 7ineq12i 3697 . 2
94, 5, 83eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:  =wceq 1395   cvv 3109  i^icin 3474  X.cxp 5002  |`cres 5006 This theorem is referenced by:  resindm  5323  gsum2dlem2  16998  gsum2dOLD  17000  fnresin  27470  resisresindm  32305 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-xp 5010  df-rel 5011  df-res 5016
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