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Theorem rel0 4889
Description: The empty set is a relation. (Contributed by NM, 26-Apr-1998.)
Assertion
Ref Expression
rel0  |-  Rel  (/)

Proof of Theorem rel0
StepHypRef Expression
1 0ss 3559 . 2  |-  (/)  C_  ( _V  X.  _V )
2 df-rel 4775 . 2  |-  ( Rel  (/) 
<->  (/)  C_  ( _V  X.  _V ) )
31, 2mpbir 200 1  |-  Rel  (/)
Colors of variables: wff set class
Syntax hints:   _Vcvv 2864    C_ wss 3228   (/)c0 3531    X. cxp 4766   Rel wrel 4773
This theorem is referenced by:  reldm0  4975  cnv0  5163  cnveq0  5209  co02  5265  co01  5266  tpos0  6348  0we1  6589  0er  6779  canthwe  8360  dibvalrel  31405  dicvalrelN  31427  dihvalrel  31521
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1930  ax-ext 2339
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2345  df-cleq 2351  df-clel 2354  df-nfc 2483  df-v 2866  df-dif 3231  df-in 3235  df-ss 3242  df-nul 3532  df-rel 4775
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