Theorem xpeq12i 4753

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 4750	. 2 |- ( ( A = B /\ C = D ) -> ( A X. C ) = ( B X. D ) )
4	1, 2, 3	mp2an 426	1 |- ( A X. C ) = ( B X. D )

Syntax hints:   = wceq 1398   X. cxp 4729

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 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-11 1555  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2213

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-nf 1510  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-opab 4156  df-xp 4737

This theorem is referenced by:  xpssres  5054  imainrect  5189  cnvssrndm  5265  txbasval  15078