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Theorem inres 5289
 Description: Move intersection into class restriction. (Contributed by NM, 18-Dec-2008.)
Assertion
Ref Expression
inres

Proof of Theorem inres
StepHypRef Expression
1 inass 3708 . 2
2 df-res 5011 . 2
3 df-res 5011 . . 3
43ineq2i 3697 . 2
51, 2, 43eqtr4ri 2507 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1379  cvv 3113   cin 3475   cxp 4997   cres 5001 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-v 3115  df-in 3483  df-res 5011 This theorem is referenced by:  resindm  5316  fninfp  6086
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