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Theorem relxp 4652
Description: A cross product is a relation. Theorem 3.13(i) of [Monk1] p. 37. (Contributed by NM, 2-Aug-1994.)
Assertion
Ref Expression
relxp  |-  Rel  ( A  X.  B )

Proof of Theorem relxp
StepHypRef Expression
1 xpss 4651 . 2  |-  ( A  X.  B )  C_  ( _V  X.  _V )
2 df-rel 4550 . 2  |-  ( Rel  ( A  X.  B
)  <->  ( A  X.  B )  C_  ( _V  X.  _V ) )
31, 2mpbir 145 1  |-  Rel  ( A  X.  B )
Colors of variables: wff set class
Syntax hints:   _Vcvv 2687    C_ wss 3072    X. cxp 4541   Rel wrel 4548
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 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122
This theorem depends on definitions:  df-bi 116  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2689  df-in 3078  df-ss 3085  df-opab 3994  df-xp 4549  df-rel 4550
This theorem is referenced by:  xpiindim  4680  eliunxp  4682  opeliunxp2  4683  relres  4851  codir  4931  qfto  4932  cnvcnv  4995  dfco2  5042  unixpm  5078  ressn  5083  fliftcnv  5700  fliftfun  5701  opeliunxp2f  6139  reltpos  6151  tpostpos  6165  tposfo  6172  tposf  6173  swoer  6461  xpider  6504  erinxp  6507  xpcomf1o  6723  ltrel  7846  lerel  7848  fisumcom2  11235  txuni2  12455  txdis1cn  12477  xmeter  12635  reldvg  12847
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