Theorem xpeq12i 4569

Description: Equality inference for cross product. (Contributed by FL, 31-Aug-2009.)

Hypotheses

Ref	Expression
xpeq12i.1	|- A = B
xpeq12i.2	|- C = D

Assertion

Ref	Expression
xpeq12i	|- ( A X. C ) = ( B X. D )

Proof of Theorem xpeq12i

Step	Hyp	Ref	Expression
1		xpeq12i.1	. 2 |- A = B
2		xpeq12i.2	. 2 |- C = D
3		xpeq12 4566	. 2 |- ( ( A = B /\ C = D ) -> ( A X. C ) = ( B X. D ) )
4	1, 2, 3	mp2an 423	1 |- ( A X. C ) = ( B X. D )

Syntax hints:   = wceq 1332   X. cxp 4545

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 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-11 1485  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122

This theorem depends on definitions:  df-bi 116  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-opab 3998  df-xp 4553

This theorem is referenced by:  xpssres  4862  imainrect  4992  cnvssrndm  5068  txbasval  12475