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Theorem xpss 4746
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 3140 . 2  |-  A  C_  _V
2 ssv 3140 . 2  |-  B  C_  _V
3 xpss12 4745 . 2  |-  ( ( A  C_  _V  /\  B  C_ 
_V )  ->  ( A  X.  B )  C_  ( _V  X.  _V )
)
41, 2, 3mp2an 656 1  |-  ( A  X.  B )  C_  ( _V  X.  _V )
Colors of variables: wff set class
Syntax hints:   _Vcvv 2740    C_ wss 3094    X. cxp 4624
This theorem is referenced by:  relxp  4747  relrelss  5148  dff3  5572  eqopi  6055  op1steq  6063  dfoprab4  6076  copsex2ga  6080  infxpenlem  7574  nqerf  8487  uzrdgfni  10952  homarel  13795  relxpchom  13882  frmdplusg  14403  upxp  17244  txprel  23760  relded  25072  relcat  25093  dihvalrel  30599
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1927  ax-ext 2237
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1884  df-clab 2243  df-cleq 2249  df-clel 2252  df-nfc 2381  df-v 2742  df-in 3101  df-ss 3108  df-opab 4018  df-xp 4640
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