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Theorem elaltxp 25812
 Description: Membership in alternate cross products. (Contributed by Scott Fenton, 23-Mar-2012.)
Assertion
Ref Expression
elaltxp
Distinct variable groups:   ,,   ,,   ,,

Proof of Theorem elaltxp
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elex 2956 . 2
2 altopex 25797 . . . . 5
3 eleq1 2495 . . . . 5
42, 3mpbiri 225 . . . 4
54a1i 11 . . 3
65rexlimivv 2827 . 2
7 eqeq1 2441 . . . 4
872rexbidv 2740 . . 3
9 df-altxp 25796 . . 3
108, 9elab2g 3076 . 2
111, 6, 10pm5.21nii 343 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359   wceq 1652   wcel 1725  wrex 2698  cvv 2948  caltop 25793   caltxp 25794 This theorem is referenced by:  altopelaltxp  25813  altxpsspw  25814 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 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 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-ne 2600  df-ral 2702  df-rex 2703  df-v 2950  df-dif 3315  df-un 3317  df-nul 3621  df-sn 3812  df-pr 3813  df-altop 25795  df-altxp 25796
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