Theorem xpeq2i 4659

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 4653	. 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 1363   X. cxp 4636

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 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-11 1516  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169

This theorem depends on definitions:  df-bi 117  df-tru 1366  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-opab 4077  df-xp 4644

This theorem is referenced by:  xpindir  4775  xpexgALT  6147  xp1en  6836  djuassen  7229  xpdjuen  7230  pwf1oexmid  15021