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Theorem rel0 4462
 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 3255 . 2 ∅ ⊆ (V × V)
2 df-rel 4352 . 2 (Rel ∅ ↔ ∅ ⊆ (V × V))
31, 2mpbir 134 1 Rel ∅
 Colors of variables: wff set class Syntax hints:  Vcvv 2557   ⊆ wss 2917  ∅c0 3224   × cxp 4343  Rel wrel 4350 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-dif 2920  df-in 2924  df-ss 2931  df-nul 3225  df-rel 4352 This theorem is referenced by:  reldm0  4553  cnv0  4727  cnveq0  4777  co02  4834  co01  4835  tpos0  5889  0er  6140
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