Theorem xpeq12i 4685

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 4682	. 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 1364   X. cxp 4661

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 1461  ax-7 1462  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-11 1520  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548  ax-i5r 1549  ax-ext 2178

This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1475  df-sb 1777  df-clab 2183  df-cleq 2189  df-clel 2192  df-opab 4095  df-xp 4669

This theorem is referenced by:  xpssres  4981  imainrect  5115  cnvssrndm  5191  txbasval  14503