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Theorem xpeq2i 4563
Description: Equality inference for cross product. (Contributed by NM, 21-Dec-2008.)
Hypothesis
Ref Expression
xpeq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
xpeq2i (𝐶 × 𝐴) = (𝐶 × 𝐵)

Proof of Theorem xpeq2i
StepHypRef Expression
1 xpeq1i.1 . 2 𝐴 = 𝐵
2 xpeq2 4557 . 2 (𝐴 = 𝐵 → (𝐶 × 𝐴) = (𝐶 × 𝐵))
31, 2ax-mp 5 1 (𝐶 × 𝐴) = (𝐶 × 𝐵)
Colors of variables: wff set class
Syntax hints:   = wceq 1331   × cxp 4540
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121
This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-opab 3993  df-xp 4548
This theorem is referenced by:  xpindir  4678  xpexgALT  6034  xp1en  6720  djuassen  7085  xpdjuen  7086  pwf1oexmid  13340
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