Theorem xpeq12 4364

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 4359	. 2 |- ( A = B -> ( A X. C ) = ( B X. C ) )
2		xpeq2 4360	. 2 |- ( C = D -> ( B X. C ) = ( B X. D ) )
3	1, 2	sylan9eq 2092	1 |- ( ( A = B /\ C = D ) -> ( A X. C ) = ( B X. D ) )

Syntax hints:   -> wi 4   /\ wa 97   = wceq 1243   X. cxp 4343

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022

This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-opab 3819  df-xp 4351

This theorem is referenced by:  xpeq12i  4367  xpeq12d  4370  xpid11m  4557  xp11m  4759