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Theorem xpeq12i 4806
 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 × C) = (B × D)

Proof of Theorem xpeq12i
StepHypRef Expression
1 xpeq12i.1 . 2 A = B
2 xpeq12i.2 . 2 C = D
3 xpeq12 4803 . 2 ((A = B C = D) → (A × C) = (B × D))
41, 2, 3mp2an 653 1 (A × C) = (B × D)
 Colors of variables: wff setvar class Syntax hints:   = 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:  rnpprod  5842
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