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Theorem relxp 4447
 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 4446 . 2 (𝐴 × 𝐵) ⊆ (V × V)
2 df-rel 4352 . 2 (Rel (𝐴 × 𝐵) ↔ (𝐴 × 𝐵) ⊆ (V × V))
31, 2mpbir 134 1 Rel (𝐴 × 𝐵)
 Colors of variables: wff set class Syntax hints:  Vcvv 2557   ⊆ wss 2917   × cxp 4343  Rel wrel 4350 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  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-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-in 2924  df-ss 2931  df-opab 3819  df-xp 4351  df-rel 4352 This theorem is referenced by:  xpiindim  4473  eliunxp  4475  opeliunxp2  4476  relres  4639  codir  4713  qfto  4714  cnvcnv  4773  dfco2  4820  unixpm  4853  ressn  4858  fliftcnv  5435  fliftfun  5436  reltpos  5865  tpostpos  5879  tposfo  5886  tposf  5887  swoer  6134  xpiderm  6177  erinxp  6180  xpcomf1o  6299  ltrel  7081  lerel  7083
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