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Theorem rel0 4664
 Description: The empty set is a relation. (Contributed by NM, 26-Apr-1998.)
Assertion
Ref Expression
rel0

Proof of Theorem rel0
StepHypRef Expression
1 0ss 3401 . 2
2 df-rel 4546 . 2
31, 2mpbir 145 1
 Colors of variables: wff set class Syntax hints:  cvv 2686   wss 3071  c0 3363   cxp 4537   wrel 4544 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-v 2688  df-dif 3073  df-in 3077  df-ss 3084  df-nul 3364  df-rel 4546 This theorem is referenced by:  reldm0  4757  cnv0  4942  cnveq0  4995  co02  5052  co01  5053  tpos0  6171  0er  6463
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