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Theorem elxp3 4890
 Description: Membership in a Cartesian product. (Contributed by NM, 5-Mar-1995.)
Assertion
Ref Expression
elxp3
Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem elxp3
StepHypRef Expression
1 elxp 4856 . 2
2 eqcom 2478 . . . 4
3 opelxp 4869 . . . 4
42, 3anbi12i 711 . . 3
542exbii 1727 . 2
61, 5bitr4i 260 1
 Colors of variables: wff setvar class Syntax hints:   wb 189   wa 376   wceq 1452  wex 1671   wcel 1904  cop 3965   cxp 4837 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-9 1913  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451  ax-sep 4518  ax-nul 4527  ax-pr 4639 This theorem depends on definitions:  df-bi 190  df-or 377  df-an 378  df-3an 1009  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-ne 2643  df-ral 2761  df-rex 2762  df-rab 2765  df-v 3033  df-dif 3393  df-un 3395  df-in 3397  df-ss 3404  df-nul 3723  df-if 3873  df-sn 3960  df-pr 3962  df-op 3966  df-opab 4455  df-xp 4845 This theorem is referenced by:  optocl  4916  unixp0  5377
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