Theorem relxp 3245

Description: A cross product is a relation. Theorem 3.13(i) of [Monk1] p. 37.

Assertion

Ref	Expression
relxp	|- Rel (A X. B)

Proof of Theorem relxp

Step	Hyp	Ref	Expression
1		xpss 3220	. 2 |- (A X. B) (_ (V X. V)
2		df-rel 3175	. 2 |- (Rel (A X. B) <-> (A X. B) (_ (V X. V))
3	1, 2	mpbir 190	1 |- Rel (A X. B)

Syntax hints:  Vcvv 1802   (_ wss 2037   X. cxp 3158  Rel wrel 3165

This theorem is referenced by:  ssxp 3246  xpsspw 3247  inxp 3259  cnvxp 3450  cnvcnv 3472  unixp 3503  fconst 3643  oprssdm 4027  ndmoprcl 4030  eloprabi 4102  ecopoprdm 4293  mapsspw 4325  mapdom2lem 4473  brdom3 4773  brdom5 4774  brdom4 4775  prcdpq 5069  ndmioo 6307  elfzlem 6405  infxpidmlem7 7501  nvvop 8166  eloi 10503

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-7 959  ax-gen 960  ax-8 961  ax-10 963  ax-11 964  ax-12 965  ax-13 966  ax-14 967  ax-17 968  ax-4 970  ax-5o 972  ax-6o 975  ax-9o 1119  ax-10o 1136  ax-16 1206  ax-11o 1213  ax-ext 1452  ax-sep 2693  ax-pow 2732  ax-pr 2769

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225  df-ex 978  df-sb 1168  df-eu 1375  df-mo 1376  df-clab 1457  df-cleq 1462  df-clel 1465  df-ne 1579  df-v 1803  df-dif 2039  df-un 2040  df-in 2041  df-ss 2043  df-nul 2271  df-pw 2392  df-sn 2402  df-pr 2403  df-op 2406  df-opab 2657  df-xp 3174  df-rel 3175

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