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Theorem rel0 4490
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 3283 . 2  |-  (/)  C_  ( _V  X.  _V )
2 df-rel 4380 . 2  |-  ( Rel  (/) 
<->  (/)  C_  ( _V  X.  _V ) )
31, 2mpbir 138 1  |-  Rel  (/)
Colors of variables: wff set class
Syntax hints:   _Vcvv 2574    C_ wss 2945   (/)c0 3252    X. cxp 4371   Rel wrel 4378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038
This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-dif 2948  df-in 2952  df-ss 2959  df-nul 3253  df-rel 4380
This theorem is referenced by:  reldm0  4581  cnv0  4755  cnveq0  4805  co02  4862  co01  4863  tpos0  5920  0er  6171
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