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Theorem elxpi 4800
 Description: Membership in a cross product. Uses fewer axioms than elxp 4801. (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 2359 . . . . . 6
21anbi1d 685 . . . . 5
322exbidv 1628 . . . 4
43elabg 2986 . . 3
54ibi 232 . 2
6 df-xp 4784 . . 3
7 df-opab 4623 . . 3
86, 7eqtri 2373 . 2
95, 8eleq2s 2445 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wa 358  wex 1541   wceq 1642   wcel 1710  cab 2339  cop 4561  copab 4622   cxp 4770 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-opab 4623  df-xp 4784 This theorem is referenced by: (None)
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