Theorem xpeq2d 4749

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 4740	. 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 1397   X. cxp 4723

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 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-11 1554  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-opab 4151  df-xp 4731

This theorem is referenced by:  csbresg  5016  fconstg  5533  fvdiagfn  6861  mapsncnv  6863  xpsneng  7005  exp3val  10802  mulgval  13708  reldvg  15402  dvfvalap  15404