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Theorem xpeq2i 4530
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 4524 . 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 1316   × cxp 4507
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 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-11 1469  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-opab 3960  df-xp 4515
This theorem is referenced by:  xpindir  4645  xpexgALT  5999  xp1en  6685  djuassen  7041  xpdjuen  7042  pwf1oexmid  13121
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