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Theorem xpm 4960
 Description: The cross product of inhabited classes is inhabited. (Contributed by Jim Kingdon, 13-Dec-2018.)
Assertion
Ref Expression
xpm
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem xpm
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 xpmlem 4959 . 2
2 eleq1 2202 . . . 4
32cbvexv 1890 . . 3
4 eleq1 2202 . . . 4
54cbvexv 1890 . . 3
63, 5anbi12i 455 . 2
7 eleq1 2202 . . 3
87cbvexv 1890 . 2
91, 6, 83bitr3i 209 1
 Colors of variables: wff set class Syntax hints:   wa 103   wb 104  wex 1468   wcel 1480   cxp 4537 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121  ax-sep 4046  ax-pow 4098  ax-pr 4131 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ral 2421  df-rex 2422  df-v 2688  df-un 3075  df-in 3077  df-ss 3084  df-pw 3512  df-sn 3533  df-pr 3534  df-op 3536  df-opab 3990  df-xp 4545 This theorem is referenced by:  ssxpbm  4974  xp11m  4977  xpexr2m  4980  unixpm  5074
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