Theorem xpeq2i 4680

Description: Equality inference for cross product. (Contributed by NM, 21-Dec-2008.)

Hypothesis

Ref	Expression
xpeq1i.1	|- A = B

Assertion

Ref	Expression
xpeq2i	|- ( C X. A ) = ( C X. B )

Proof of Theorem xpeq2i

Step	Hyp	Ref	Expression
1		xpeq1i.1	. 2 |- A = B
2		xpeq2 4674	. 2 |- ( A = B -> ( C X. A ) = ( C X. B ) )
3	1, 2	ax-mp 5	1 |- ( C X. A ) = ( C X. B )

Syntax hints:   = wceq 1364   X. cxp 4657

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 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-11 1517  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2175

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2180  df-cleq 2186  df-clel 2189  df-opab 4091  df-xp 4665

This theorem is referenced by:  xpindir  4798  xpexgALT  6185  xp1en  6877  djuassen  7277  xpdjuen  7278  pwf1oexmid  15490