Theorem xpeq2d 4571

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

Step	Hyp	Ref	Expression
1		xpeq1d.1	. 2 |- ( ph -> A = B )
2		xpeq2 4562	. 2 |- ( A = B -> ( C X. A ) = ( C X. B ) )
3	1, 2	syl 14	1 |- ( ph -> ( C X. A ) = ( C X. B ) )

Syntax hints:   -> wi 4   = wceq 1332   X. cxp 4545

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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-opab 3998  df-xp 4553

This theorem is referenced by:  csbresg  4830  fconstg  5327  fvdiagfn  6595  mapsncnv  6597  xpsneng  6724  exp3val  10326  reldvg  12856  dvfvalap  12858