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Theorem rabxp 5041
Description: Membership in a class builder restricted to a Cartesian product. (Contributed by NM, 20-Feb-2014.)
Hypothesis
Ref Expression
rabxp.1
Assertion
Ref Expression
rabxp
Distinct variable groups:   , , ,   , , ,   , ,   ,

Proof of Theorem rabxp
StepHypRef Expression
1 elxp 5021 . . . . 5
21anbi1i 695 . . . 4
3 19.41vv 1772 . . . 4
4 anass 649 . . . . . 6
5 rabxp.1 . . . . . . . . 9
65anbi2d 703 . . . . . . . 8
7 df-3an 975 . . . . . . . 8
86, 7syl6bbr 263 . . . . . . 7
98pm5.32i 637 . . . . . 6
104, 9bitri 249 . . . . 5
11102exbii 1668 . . . 4
122, 3, 113bitr2i 273 . . 3
1312abbii 2591 . 2
14 df-rab 2816 . 2
15 df-opab 4511 . 2
1613, 14, 153eqtr4i 2496 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  =wceq 1395  E.wex 1612  e.wcel 1818  {cab 2442  {crab 2811  <.cop 4035  {copab 4509  X.cxp 5002
This theorem is referenced by:  fgraphxp  31171  cicer  32590  dib1dim  36892  diclspsn  36921
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-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
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