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Theorem relxp 4560
Description: A cross product is a relation. Theorem 3.13(i) of [Monk1] p. 37. (Contributed by NM, 2-Aug-1994.)
Assertion
Ref Expression
relxp Rel (𝐴 × 𝐵)

Proof of Theorem relxp
StepHypRef Expression
1 xpss 4559 . 2 (𝐴 × 𝐵) ⊆ (V × V)
2 df-rel 4459 . 2 (Rel (𝐴 × 𝐵) ↔ (𝐴 × 𝐵) ⊆ (V × V))
31, 2mpbir 145 1 Rel (𝐴 × 𝐵)
Colors of variables: wff set class
Syntax hints:  Vcvv 2620  wss 3000   × cxp 4450  Rel wrel 4457
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071
This theorem depends on definitions:  df-bi 116  df-nf 1396  df-sb 1694  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-v 2622  df-in 3006  df-ss 3013  df-opab 3906  df-xp 4458  df-rel 4459
This theorem is referenced by:  xpiindim  4586  eliunxp  4588  opeliunxp2  4589  relres  4754  codir  4833  qfto  4834  cnvcnv  4896  dfco2  4943  unixpm  4979  ressn  4984  fliftcnv  5588  fliftfun  5589  opeliunxp2f  6017  reltpos  6029  tpostpos  6043  tposfo  6050  tposf  6051  swoer  6334  xpiderm  6377  erinxp  6380  xpcomf1o  6595  ltrel  7609  lerel  7611  fisumcom2  10893
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