Theorem xpeq1i 4713

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 4707	. 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 4691

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 1471  ax-7 1472  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-8 1528  ax-11 1530  ax-4 1534  ax-17 1550  ax-i9 1554  ax-ial 1558  ax-i5r 1559  ax-ext 2189

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1485  df-sb 1787  df-clab 2194  df-cleq 2200  df-clel 2203  df-opab 4122  df-xp 4699

This theorem is referenced by:  iunxpconst  4753  xpindi  4831  resdmres  5193  mapsnconst  6804  mapsncnv  6805  xp2dju  7358