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Theorem rel0 4958
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 3616 . 2  |-  (/)  C_  ( _V  X.  _V )
2 df-rel 4844 . 2  |-  ( Rel  (/) 
<->  (/)  C_  ( _V  X.  _V ) )
31, 2mpbir 201 1  |-  Rel  (/)
Colors of variables: wff set class
Syntax hints:   _Vcvv 2916    C_ wss 3280   (/)c0 3588    X. cxp 4835   Rel wrel 4842
This theorem is referenced by:  reldm0  5046  cnv0  5234  cnveq0  5286  co02  5342  co01  5343  tpos0  6468  0we1  6709  0er  6899  canthwe  8482  dibvalrel  31646  dicvalrelN  31668  dihvalrel  31762
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2385
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2391  df-cleq 2397  df-clel 2400  df-nfc 2529  df-v 2918  df-dif 3283  df-in 3287  df-ss 3294  df-nul 3589  df-rel 4844
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