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Theorem relxp 4535
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 4534 . 2 (𝐴 × 𝐵) ⊆ (V × V)
2 df-rel 4435 . 2 (Rel (𝐴 × 𝐵) ↔ (𝐴 × 𝐵) ⊆ (V × V))
31, 2mpbir 144 1 Rel (𝐴 × 𝐵)
Colors of variables: wff set class
Syntax hints:  Vcvv 2619  wss 2997   × cxp 4426  Rel wrel 4433
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-in 3003  df-ss 3010  df-opab 3892  df-xp 4434  df-rel 4435
This theorem is referenced by:  xpiindim  4561  eliunxp  4563  opeliunxp2  4564  relres  4728  codir  4807  qfto  4808  cnvcnv  4870  dfco2  4917  unixpm  4953  ressn  4958  fliftcnv  5556  fliftfun  5557  opeliunxp2f  5985  reltpos  5997  tpostpos  6011  tposfo  6018  tposf  6019  swoer  6300  xpiderm  6343  erinxp  6346  xpcomf1o  6521  ltrel  7527  lerel  7529  fisumcom2  10795
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