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Theorem xpss 4809
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 3211 . 2  |-  A  C_  _V
2 ssv 3211 . 2  |-  B  C_  _V
3 xpss12 4808 . 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 2801    C_ wss 3165    X. cxp 4703
This theorem is referenced by:  relxp  4810  relrelss  5212  dff3  5689  eqopi  6172  op1steq  6180  dfoprab4  6193  copsex2ga  6197  infxpenlem  7657  nqerf  8570  uzrdgfni  11037  homarel  13884  relxpchom  13971  frmdplusg  14492  upxp  17333  xppreima2  23227  xpinpreima2  23306  tpr2rico  23311  txprel  24490  relded  25843  relcat  25864  dihvalrel  32091
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-in 3172  df-ss 3179  df-opab 4094  df-xp 4711
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