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Theorem xpeq12i 4310
Description: Equality inference for cross product. (Contributed by FL, 31-Aug-2009.)
Hypotheses
Ref Expression
xpeq12i.1
xpeq12i.2  C  D
Assertion
Ref Expression
xpeq12i  X.  C  X.  D

Proof of Theorem xpeq12i
StepHypRef Expression
1 xpeq12i.1 . 2
2 xpeq12i.2 . 2  C  D
3 xpeq12 4307 . 2  C  D  X.  C  X.  D
41, 2, 3mp2an 402 1  X.  C  X.  D
Colors of variables: wff set class
Syntax hints:   wceq 1242    X. cxp 4286
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 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-tru 1245  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-opab 3810  df-xp 4294
This theorem is referenced by:  xpssres  4588  imainrect  4709  cnvssrndm  4785
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