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Theorem xpss 4973
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 3360 . 2  |-  A  C_  _V
2 ssv 3360 . 2  |-  B  C_  _V
3 xpss12 4972 . 2  |-  ( ( A  C_  _V  /\  B  C_ 
_V )  ->  ( A  X.  B )  C_  ( _V  X.  _V )
)
41, 2, 3mp2an 654 1  |-  ( A  X.  B )  C_  ( _V  X.  _V )
Colors of variables: wff set class
Syntax hints:   _Vcvv 2948    C_ wss 3312    X. cxp 4867
This theorem is referenced by:  relxp  4974  eqbrrdva  5033  relrelss  5384  dff3  5873  eqopi  6374  op1steq  6382  dfoprab4  6395  copsex2ga  6399  infxpenlem  7884  nqerf  8796  uzrdgfni  11286  homarel  14179  relxpchom  14266  frmdplusg  14787  upxp  17643  ustrel  18229  utop2nei  18268  utop3cls  18269  fmucndlem  18309  metustrelOLD  18573  metustrel  18574  xppreima2  24048  df1stres  24079  df2ndres  24080  metideq  24276  metider  24277  pstmfval  24279  xpinpreima2  24293  tpr2rico  24298  dya2iocnrect  24619  txprel  25674  mblfinlem  26190  dihvalrel  31916
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-in 3319  df-ss 3326  df-opab 4259  df-xp 4875
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