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Theorem xpss 4793
Description: A cross product is included in the ordered pair universe. Exercise 3 of [TakeutiZaring] p. 25. (Contributed by NM, 2-Aug-1994.)
Assertion
Ref Expression
xpss  |-  ( A  X.  B )  C_  ( _V  X.  _V )

Proof of Theorem xpss
StepHypRef Expression
1 ssv 3198 . 2  |-  A  C_  _V
2 ssv 3198 . 2  |-  B  C_  _V
3 xpss12 4792 . 2  |-  ( ( A  C_  _V  /\  B  C_ 
_V )  ->  ( A  X.  B )  C_  ( _V  X.  _V )
)
41, 2, 3mp2an 653 1  |-  ( A  X.  B )  C_  ( _V  X.  _V )
Colors of variables: wff set class
Syntax hints:   _Vcvv 2788    C_ wss 3152    X. cxp 4687
This theorem is referenced by:  relxp  4794  relrelss  5196  dff3  5673  eqopi  6156  op1steq  6164  dfoprab4  6177  copsex2ga  6181  infxpenlem  7641  nqerf  8554  uzrdgfni  11021  homarel  13868  relxpchom  13955  frmdplusg  14476  upxp  17317  xppreima2  23212  xpinpreima2  23291  tpr2rico  23296  txprel  24419  relded  25740  relcat  25761  dihvalrel  31469
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-in 3159  df-ss 3166  df-opab 4078  df-xp 4695
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