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Theorem relxp 4390
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 4389 . 2 (A × B) ⊆ (V × V)
2 df-rel 4295 . 2 (Rel (A × B) ↔ (A × B) ⊆ (V × V))
31, 2mpbir 134 1 Rel (A × B)
Colors of variables: wff set class
Syntax hints:  Vcvv 2551  wss 2911   × cxp 4286  Rel wrel 4293
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 629  ax-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-10 1393  ax-11 1394  ax-i12 1395  ax-bnd 1396  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-nfc 2164  df-v 2553  df-in 2918  df-ss 2925  df-opab 3810  df-xp 4294  df-rel 4295
This theorem is referenced by:  xpiindim  4416  eliunxp  4418  opeliunxp2  4419  relres  4582  codir  4656  qfto  4657  cnvcnv  4716  dfco2  4763  unixpm  4796  ressn  4801  fliftcnv  5378  fliftfun  5379  reltpos  5806  tpostpos  5820  tposfo  5827  tposf  5828  swoer  6070  xpiderm  6113  erinxp  6116  xpcomf1o  6235  ltrel  6838  lerel  6840
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