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Theorem xpeq12 4307
 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 4302 . 2 (A = B → (A × 𝐶) = (B × 𝐶))
2 xpeq2 4303 . 2 (𝐶 = 𝐷 → (B × 𝐶) = (B × 𝐷))
31, 2sylan9eq 2089 1 ((A = B 𝐶 = 𝐷) → (A × 𝐶) = (B × 𝐷))
 Colors of variables: wff set class Syntax hints:   → wi 4   ∧ wa 97   = wceq 1242   × 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:  xpeq12i  4310  xpeq12d  4313  xpid11m  4500  xp11m  4702
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