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Theorem xpeq1i 4433
Description: Equality inference for cross product. (Contributed by NM, 21-Dec-2008.)
Hypothesis
Ref Expression
xpeq1i.1  |-  A  =  B
Assertion
Ref Expression
xpeq1i  |-  ( A  X.  C )  =  ( B  X.  C
)

Proof of Theorem xpeq1i
StepHypRef Expression
1 xpeq1i.1 . 2  |-  A  =  B
2 xpeq1 4427 . 2  |-  ( A  =  B  ->  ( A  X.  C )  =  ( B  X.  C
) )
31, 2ax-mp 7 1  |-  ( A  X.  C )  =  ( B  X.  C
)
Colors of variables: wff set class
Syntax hints:    = wceq 1287    X. cxp 4411
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-11 1440  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-opab 3877  df-xp 4419
This theorem is referenced by:  iunxpconst  4468  xpindi  4541  resdmres  4890  mapsnconst  6405  mapsncnv  6406
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