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Theorem xpeq1d 4860
Description: Equality deduction for cross product. (Contributed by Jeff Madsen, 17-Jun-2010.)
Hypothesis
Ref Expression
xpeq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
xpeq1d  |-  ( ph  ->  ( A  X.  C
)  =  ( B  X.  C ) )

Proof of Theorem xpeq1d
StepHypRef Expression
1 xpeq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 xpeq1 4851 . 2  |-  ( A  =  B  ->  ( A  X.  C )  =  ( B  X.  C
) )
31, 2syl 16 1  |-  ( ph  ->  ( A  X.  C
)  =  ( B  X.  C ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1649    X. cxp 4835
This theorem is referenced by:  xpssres  5139  curry1  6397  fparlem3  6407  fparlem4  6408  ixpsnf1o  7061  xpfi  7337  dfac5lem3  7962  dfac5lem4  7963  cdaassen  8018  hashxplem  11651  subgga  15032  gasubg  15034  sylow2blem2  15210  psrval  16384  txindislem  17618  txtube  17625  txcmplem1  17626  txhaus  17632  xkoinjcn  17672  pt1hmeo  17791  tsmsxplem1  18135  tsmsxplem2  18136  cnmpt2pc  18906  mpfrcl  19892  evlsval  19893  dchrval  20971  0ofval  22241  esumcvg  24429  sxbrsigalem0  24574  sxbrsigalem3  24575  sxbrsigalem2  24589  axlowdimlem15  25799  axlowdim  25804  sdclem1  26337  ismrer1  26437  mzpclval  26672  mamufval  27311  mendval  27359  ldualset  29608  dibval  31625  dibval3N  31629  dib0  31647  dihwN  31772  hdmap1fval  32280
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-opab 4227  df-xp 4843
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