Theorem xpeq1i 4629

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 4623	. 2 |- ( A = B -> ( A X. C ) = ( B X. C ) )
3	1, 2	ax-mp 5	1 |- ( A X. C ) = ( B X. C )

Syntax hints:   = wceq 1348   X. cxp 4607

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-7 1441  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-8 1497  ax-11 1499  ax-4 1503  ax-17 1519  ax-i9 1523  ax-ial 1527  ax-i5r 1528  ax-ext 2152

This theorem depends on definitions:  df-bi 116  df-tru 1351  df-nf 1454  df-sb 1756  df-clab 2157  df-cleq 2163  df-clel 2166  df-opab 4049  df-xp 4615

This theorem is referenced by:  iunxpconst  4669  xpindi  4744  resdmres  5100  mapsnconst  6668  mapsncnv  6669  xp2dju  7179