Theorem xpeq2i 4740

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 4734	. 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 1395   X. cxp 4717

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 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-11 1552  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-opab 4146  df-xp 4725

This theorem is referenced by:  xpindir  4858  xpexgALT  6278  xp1en  6982  djuassen  7399  xpdjuen  7400  pwf1oexmid  16365