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Theorem xpeq1i 4365
 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 4359 . 2 (𝐴 = 𝐵 → (𝐴 × 𝐶) = (𝐵 × 𝐶))
31, 2ax-mp 7 1 (𝐴 × 𝐶) = (𝐵 × 𝐶)
 Colors of variables: wff set class Syntax hints:   = wceq 1243   × cxp 4343 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 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-opab 3819  df-xp 4351 This theorem is referenced by:  iunxpconst  4400  xpindi  4471  resdmres  4812
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