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Theorem xpeq1d 4649
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 4640 . 2  |-  ( A  =  B  ->  ( A  X.  C )  =  ( B  X.  C
) )
31, 2syl 14 1  |-  ( ph  ->  ( A  X.  C
)  =  ( B  X.  C ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1353    X. cxp 4624
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 4065  df-xp 4632
This theorem is referenced by:  xpssres  4942  ixpsnf1o  6735  xpfi  6928  hashxp  10801
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