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Theorem rabxp 4914
 Description: Membership in a class builder restricted to a cross product. (Contributed by NM, 20-Feb-2014.)
Hypothesis
Ref Expression
rabxp.1
Assertion
Ref Expression
rabxp
Distinct variable groups:   ,,,   ,,,   ,,   ,
Allowed substitution hints:   ()   (,)

Proof of Theorem rabxp
StepHypRef Expression
1 elxp 4895 . . . . 5
21anbi1i 677 . . . 4
3 19.41vv 1925 . . . 4
4 anass 631 . . . . . 6
5 rabxp.1 . . . . . . . . 9
65anbi2d 685 . . . . . . . 8
7 df-3an 938 . . . . . . . 8
86, 7syl6bbr 255 . . . . . . 7
98pm5.32i 619 . . . . . 6
104, 9bitri 241 . . . . 5
11102exbii 1593 . . . 4
122, 3, 113bitr2i 265 . . 3
1312abbii 2548 . 2
14 df-rab 2714 . 2
15 df-opab 4267 . 2
1613, 14, 153eqtr4i 2466 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   w3a 936  wex 1550   wceq 1652   wcel 1725  cab 2422  crab 2709  cop 3817  copab 4265   cxp 4876 This theorem is referenced by:  fgraphxp  27507  dib1dim  31963  diclspsn  31992 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417  ax-sep 4330  ax-nul 4338  ax-pr 4403 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  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-ne 2601  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-opab 4267  df-xp 4884
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