Theorem relxp 4495

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 X. B )

Proof of Theorem relxp

Step	Hyp	Ref	Expression
1		xpss 4494	. 2 |- ( A X. B ) C_ ( _V X. _V )
2		df-rel 4398	. 2 |- ( Rel ( A X. B ) <-> ( A X. B ) C_ ( _V X. _V ) )
3	1, 2	mpbir 144	1 |- Rel ( A X. B )

Syntax hints:   _Vcvv 2610   C_ wss 2982   X. cxp 4389   Rel wrel 4396

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 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065

This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-in 2988  df-ss 2995  df-opab 3860  df-xp 4397  df-rel 4398

This theorem is referenced by:  xpiindim  4521  eliunxp  4523  opeliunxp2  4524  relres  4687  codir  4763  qfto  4764  cnvcnv  4823  dfco2  4870  unixpm  4903  ressn  4908  fliftcnv  5486  fliftfun  5487  reltpos  5919  tpostpos  5933  tposfo  5940  tposf  5941  swoer  6221  xpiderm  6264  erinxp  6267  xpcomf1o  6390  ltrel  7293  lerel  7295