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Theorem xpeq12i 4649
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 4646 . 2  |-  ( ( A  =  B  /\  C  =  D )  ->  ( A  X.  C
)  =  ( B  X.  D ) )
41, 2, 3mp2an 426 1  |-  ( A  X.  C )  =  ( B  X.  D
)
Colors of variables: wff set class
Syntax hints:    = wceq 1353    X. cxp 4625
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-opab 4066  df-xp 4633
This theorem is referenced by:  xpssres  4943  imainrect  5075  cnvssrndm  5151  txbasval  13770
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