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Theorem xpeq12i 4713
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 4710 . 2  |-  ( ( A  =  B  /\  C  =  D )  ->  ( A  X.  C
)  =  ( B  X.  D ) )
41, 2, 3mp2an 653 1  |-  ( A  X.  C )  =  ( B  X.  D
)
Colors of variables: wff set class
Syntax hints:    = wceq 1625    X. cxp 4689
This theorem is referenced by:  xpssres  4991  imainrect  5121  cnvssrndm  5196  fpar  6224  canthwelem  8274  pjpm  16610  txbasval  17303  hausdiag  17341  ex-xp  20825  ismgm  20989  ghsubgolem  21039  hh0oi  22485  vecval1b  25462  vecval3b  25463  nds  26161  isdrngo1  26598
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1535  ax-5 1546  ax-17 1605  ax-9 1637  ax-8 1645  ax-6 1705  ax-7 1710  ax-11 1717  ax-12 1868  ax-ext 2266
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1531  df-nf 1534  df-sb 1632  df-clab 2272  df-cleq 2278  df-clel 2281  df-opab 4080  df-xp 4697
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