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Theorem dmxpm 4799
 Description: The domain of a cross product. Part of Theorem 3.13(x) of [Monk1] p. 37. (Contributed by NM, 28-Jul-1995.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
dmxpm
Distinct variable group:   ,
Allowed substitution hint:   ()

Proof of Theorem dmxpm
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 eleq1 2217 . . 3
21cbvexv 1895 . 2
3 df-xp 4585 . . . 4
43dmeqi 4780 . . 3
5 id 19 . . . . 5
65ralrimivw 2528 . . . 4
7 dmopab3 4792 . . . 4
86, 7sylib 121 . . 3
94, 8syl5eq 2199 . 2
102, 9sylbi 120 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wceq 1332  wex 1469   wcel 2125  wral 2432  copab 4020   cxp 4577   cdm 4579 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-10 1482  ax-11 1483  ax-i12 1484  ax-bndl 1486  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511  ax-i5r 1512  ax-14 2128  ax-ext 2136  ax-sep 4078  ax-pow 4130  ax-pr 4164 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1740  df-eu 2006  df-mo 2007  df-clab 2141  df-cleq 2147  df-clel 2150  df-nfc 2285  df-ral 2437  df-v 2711  df-un 3102  df-in 3104  df-ss 3111  df-pw 3541  df-sn 3562  df-pr 3563  df-op 3565  df-br 3962  df-opab 4022  df-xp 4585  df-dm 4589 This theorem is referenced by:  rnxpm  5008  ssxpbm  5014  ssxp1  5015  xpexr2m  5020  relrelss  5105  unixpm  5114  exmidfodomrlemim  7115
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