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Theorem xpeq1i 4901
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 4895 . 2  |-  ( A  =  B  ->  ( A  X.  C )  =  ( B  X.  C
) )
31, 2ax-mp 5 1  |-  ( A  X.  C )  =  ( B  X.  C
)
Colors of variables: wff set class
Syntax hints:    = wceq 1653    X. cxp 4879
This theorem is referenced by:  iunxpconst  4937  xpindi  5011  resdmres  5364  difxp2  6385  curry2  6444  mapsnconst  7062  mapsncnv  7063  cda1dif  8061  cdaassen  8067  infcda1  8078  geomulcvg  12658  hofcl  14361  ovoliunnul  19408  vitalilem5  19509  evlsval  19945  lgam1  24853  matvsca2  27469  mendvscafval  27489
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-opab 4270  df-xp 4887
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