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Theorem xpeq12i 4892
Description: Equality inference for cross product. (Contributed by FL, 31-Aug-2009.)
Hypotheses
Ref Expression
xpeq12i.1  |-  A  =  B
xpeq12i.2  |-  C  =  D
Assertion
Ref Expression
xpeq12i  |-  ( A  X.  C )  =  ( B  X.  D
)

Proof of Theorem xpeq12i
StepHypRef Expression
1 xpeq12i.1 . 2  |-  A  =  B
2 xpeq12i.2 . 2  |-  C  =  D
3 xpeq12 4889 . 2  |-  ( ( A  =  B  /\  C  =  D )  ->  ( A  X.  C
)  =  ( B  X.  D ) )
41, 2, 3mp2an 654 1  |-  ( A  X.  C )  =  ( B  X.  D
)
Colors of variables: wff set class
Syntax hints:    = wceq 1652    X. cxp 4868
This theorem is referenced by:  xpssres  5172  imainrect  5304  cnvssrndm  5383  fpar  6442  canthwelem  8517  pjpm  16927  txbasval  17630  hausdiag  17669  ussval  18281  ex-xp  21736  ismgm  21900  ghsubgolem  21950  hh0oi  23398  sitgclg  24648  sitmcl  24655  isdrngo1  26563
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-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-opab 4259  df-xp 4876
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