Theorem xpeq1i 4433

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

Hypothesis

Ref	Expression
xpeq1i.1	|- A = B

Assertion

Ref	Expression
xpeq1i	|- ( A X. C ) = ( B X. C )

Proof of Theorem xpeq1i

Step	Hyp	Ref	Expression
1		xpeq1i.1	. 2 |- A = B
2		xpeq1 4427	. 2 |- ( A = B -> ( A X. C ) = ( B X. C ) )
3	1, 2	ax-mp 7	1 |- ( A X. C ) = ( B X. C )

Syntax hints:   = wceq 1287   X. cxp 4411

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-11 1440  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067

This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-opab 3877  df-xp 4419

This theorem is referenced by:  iunxpconst  4468  xpindi  4541  resdmres  4890  mapsnconst  6405  mapsncnv  6406