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Theorem xpss 4700
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 3119 . 2  |-  A  C_  _V
2 ssv 3119 . 2  |-  B  C_  _V
3 xpss12 4699 . 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 2727    C_ wss 3078    X. cxp 4578
This theorem is referenced by:  relxp  4701  relrelss  5102  dff3  5525  eqopi  6008  op1steq  6016  dfoprab4  6029  copsex2ga  6033  infxpenlem  7525  nqerf  8434  uzrdgfni  10899  homarel  13712  relxpchom  13799  frmdplusg  14311  upxp  17149  txprel  23594  relded  24906  relcat  24927  dihvalrel  30158
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 1926  ax-ext 2234
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 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-v 2729  df-in 3085  df-ss 3089  df-opab 3975  df-xp 4594
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