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Theorem elxpi 4886
 Description: Membership in a cross product. Uses fewer axioms than elxp 4887. (Contributed by NM, 4-Jul-1994.)
Assertion
Ref Expression
elxpi
Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem elxpi
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eqeq1 2441 . . . . . 6
21anbi1d 686 . . . . 5
322exbidv 1638 . . . 4
43elabg 3075 . . 3
54ibi 233 . 2
6 df-xp 4876 . . 3
7 df-opab 4259 . . 3
86, 7eqtri 2455 . 2
95, 8eleq2s 2527 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 359  wex 1550   wceq 1652   wcel 1725  cab 2421  cop 3809  copab 4257   cxp 4868 This theorem is referenced by:  xpsspw  4978 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 2416 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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-opab 4259  df-xp 4876
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