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Theorem xpeq2d 4435
Description: Equality deduction for cross product. (Contributed by Jeff Madsen, 17-Jun-2010.)
Hypothesis
Ref Expression
xpeq1d.1 (𝜑𝐴 = 𝐵)
Assertion
Ref Expression
xpeq2d (𝜑 → (𝐶 × 𝐴) = (𝐶 × 𝐵))

Proof of Theorem xpeq2d
StepHypRef Expression
1 xpeq1d.1 . 2 (𝜑𝐴 = 𝐵)
2 xpeq2 4426 . 2 (𝐴 = 𝐵 → (𝐶 × 𝐴) = (𝐶 × 𝐵))
31, 2syl 14 1 (𝜑 → (𝐶 × 𝐴) = (𝐶 × 𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1287   × cxp 4409
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-11 1440  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-opab 3875  df-xp 4417
This theorem is referenced by:  csbresg  4684  fconstg  5170  fvdiagfn  6402  mapsncnv  6404  xpsneng  6490  expival  9855
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