Theorem xpeq2i 4649

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 4643	. 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 1353   X. cxp 4626

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-opab 4067  df-xp 4634

This theorem is referenced by:  xpindir  4765  xpexgALT  6136  xp1en  6825  djuassen  7218  xpdjuen  7219  pwf1oexmid  14834