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Theorem xpeq1i 4527
Description: Equality inference for cross product. (Contributed by NM, 21-Dec-2008.)
Hypothesis
Ref Expression
xpeq1i.1 𝐴 = 𝐵
Assertion
Ref Expression
xpeq1i (𝐴 × 𝐶) = (𝐵 × 𝐶)

Proof of Theorem xpeq1i
StepHypRef Expression
1 xpeq1i.1 . 2 𝐴 = 𝐵
2 xpeq1 4521 . 2 (𝐴 = 𝐵 → (𝐴 × 𝐶) = (𝐵 × 𝐶))
31, 2ax-mp 5 1 (𝐴 × 𝐶) = (𝐵 × 𝐶)
Colors of variables: wff set class
Syntax hints:   = wceq 1314   × cxp 4505
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 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-11 1467  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-opab 3958  df-xp 4513
This theorem is referenced by:  iunxpconst  4567  xpindi  4642  resdmres  4998  mapsnconst  6554  mapsncnv  6555  xp2dju  7035
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