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Theorem xpss 4767
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 3159 . 2  |-  A  C_  _V
2 ssv 3159 . 2  |-  B  C_  _V
3 xpss12 4766 . 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 2757    C_ wss 3113    X. cxp 4645
This theorem is referenced by:  relxp  4768  relrelss  5169  dff3  5593  eqopi  6076  op1steq  6084  dfoprab4  6097  copsex2ga  6101  infxpenlem  7595  nqerf  8508  uzrdgfni  10973  homarel  13816  relxpchom  13903  frmdplusg  14424  upxp  17265  txprel  23781  relded  25093  relcat  25114  dihvalrel  30620
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 2759  df-in 3120  df-ss 3127  df-opab 4038  df-xp 4661
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