Theorem xpeq1i 4695

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 4689	. 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 1373   X. cxp 4673

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 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-11 1529  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-opab 4106  df-xp 4681

This theorem is referenced by:  iunxpconst  4735  xpindi  4813  resdmres  5174  mapsnconst  6781  mapsncnv  6782  xp2dju  7327