Theorem xpeq12 4646

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

Assertion

Ref	Expression
xpeq12	|- ( ( A = B /\ C = D ) -> ( A X. C ) = ( B X. D ) )

Proof of Theorem xpeq12

Step	Hyp	Ref	Expression
1		xpeq1 4641	. 2 |- ( A = B -> ( A X. C ) = ( B X. C ) )
2		xpeq2 4642	. 2 |- ( C = D -> ( B X. C ) = ( B X. D ) )
3	1, 2	sylan9eq 2230	1 |- ( ( A = B /\ C = D ) -> ( A X. C ) = ( B X. D ) )

Syntax hints:   -> wi 4   /\ wa 104   = wceq 1353   X. cxp 4625

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 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-11 1506  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-opab 4066  df-xp 4633

This theorem is referenced by:  xpeq12i  4649  xpeq12d  4652  xpid11  4851  xp11m  5068  tapeq2  7252  txtopon  13765  txbasval  13770  ismet  13847  isxmet  13848