ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  xpeq2d Unicode version

Theorem xpeq2d 4558
Description: Equality deduction for cross product. (Contributed by Jeff Madsen, 17-Jun-2010.)
Hypothesis
Ref Expression
xpeq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
xpeq2d  |-  ( ph  ->  ( C  X.  A
)  =  ( C  X.  B ) )

Proof of Theorem xpeq2d
StepHypRef Expression
1 xpeq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 xpeq2 4549 . 2  |-  ( A  =  B  ->  ( C  X.  A )  =  ( C  X.  B
) )
31, 2syl 14 1  |-  ( ph  ->  ( C  X.  A
)  =  ( C  X.  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1331    X. cxp 4532
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-opab 3985  df-xp 4540
This theorem is referenced by:  csbresg  4817  fconstg  5314  fvdiagfn  6580  mapsncnv  6582  xpsneng  6709  exp3val  10288  reldvg  12806  dvfvalap  12808
  Copyright terms: Public domain W3C validator