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Theorem relxp 4474
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 4473 . 2 (𝐴 × 𝐵) ⊆ (V × V)
2 df-rel 4379 . 2 (Rel (𝐴 × 𝐵) ↔ (𝐴 × 𝐵) ⊆ (V × V))
31, 2mpbir 138 1 Rel (𝐴 × 𝐵)
Colors of variables: wff set class
Syntax hints:  Vcvv 2574  wss 2944   × cxp 4370  Rel wrel 4377
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-in 2951  df-ss 2958  df-opab 3846  df-xp 4378  df-rel 4379
This theorem is referenced by:  xpiindim  4500  eliunxp  4502  opeliunxp2  4503  relres  4666  codir  4740  qfto  4741  cnvcnv  4800  dfco2  4847  unixpm  4880  ressn  4885  fliftcnv  5462  fliftfun  5463  reltpos  5895  tpostpos  5909  tposfo  5916  tposf  5917  swoer  6164  xpiderm  6207  erinxp  6210  xpcomf1o  6329  ltrel  7139  lerel  7141
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