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Theorem rel0 5002
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 3658 . 2  |-  (/)  C_  ( _V  X.  _V )
2 df-rel 4888 . 2  |-  ( Rel  (/) 
<->  (/)  C_  ( _V  X.  _V ) )
31, 2mpbir 202 1  |-  Rel  (/)
Colors of variables: wff set class
Syntax hints:   _Vcvv 2958    C_ wss 3322   (/)c0 3630    X. cxp 4879   Rel wrel 4886
This theorem is referenced by:  reldm0  5090  cnv0  5278  cnveq0  5330  co02  5386  co01  5387  tpos0  6512  0we1  6753  0er  6943  canthwe  8531  dibvalrel  32035  dicvalrelN  32057  dihvalrel  32151
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-dif 3325  df-in 3329  df-ss 3336  df-nul 3631  df-rel 4888
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