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Theorem inres 5164
 Description: Move intersection into class restriction. (Contributed by NM, 18-Dec-2008.)
Assertion
Ref Expression
inres

Proof of Theorem inres
StepHypRef Expression
1 inass 3551 . 2
2 df-res 4890 . 2
3 df-res 4890 . . 3
43ineq2i 3539 . 2
51, 2, 43eqtr4ri 2467 1
 Colors of variables: wff set class Syntax hints:   wceq 1652  cvv 2956   cin 3319   cxp 4876   cres 4880 This theorem is referenced by:  fninfp  26735 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-in 3327  df-res 4890
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