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Theorem xpeq12 4803
 Description: Equality theorem for cross product. (Contributed by FL, 31-Aug-2009.)
Assertion
Ref Expression
xpeq12 ((A = B C = D) → (A × C) = (B × D))

Proof of Theorem xpeq12
StepHypRef Expression
1 xpeq1 4798 . 2 (A = B → (A × C) = (B × C))
2 xpeq2 4799 . 2 (C = D → (B × C) = (B × D))
31, 2sylan9eq 2405 1 ((A = B C = D) → (A × C) = (B × D))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 358   = wceq 1642   × cxp 4770 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-opab 4623  df-xp 4784 This theorem is referenced by:  xpeq12i  4806  xpeq12d  4809  xpid11  4926  xp11  5056  fnpprod  5843  mucnc  6131
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