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Theorem relxp 4737
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 4736 . 2  |-  ( A  X.  B )  C_  ( _V  X.  _V )
2 df-rel 4635 . 2  |-  ( Rel  ( A  X.  B
)  <->  ( A  X.  B )  C_  ( _V  X.  _V ) )
31, 2mpbir 146 1  |-  Rel  ( A  X.  B )
Colors of variables: wff set class
Syntax hints:   _Vcvv 2739    C_ wss 3131    X. cxp 4626   Rel wrel 4633
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2741  df-in 3137  df-ss 3144  df-opab 4067  df-xp 4634  df-rel 4635
This theorem is referenced by:  xpiindim  4766  eliunxp  4768  opeliunxp2  4769  relres  4937  restidsing  4965  codir  5019  qfto  5020  cnvcnv  5083  dfco2  5130  unixpm  5166  ressn  5171  fliftcnv  5798  fliftfun  5799  opeliunxp2f  6241  reltpos  6253  tpostpos  6267  tposfo  6274  tposf  6275  swoer  6565  xpider  6608  erinxp  6611  xpcomf1o  6827  ltrel  8021  lerel  8023  fisumcom2  11448  fprodcom2fi  11636  txuni2  13795  txdis1cn  13817  xmeter  13975  reldvg  14187
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