Theorem xpeq1i 4554

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 4548	. 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 1331   X. cxp 4532

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 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119

This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-opab 3985  df-xp 4540

This theorem is referenced by:  iunxpconst  4594  xpindi  4669  resdmres  5025  mapsnconst  6581  mapsncnv  6582  xp2dju  7064