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Theorem rel0 4550
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 3318 . 2 ∅ ⊆ (V × V)
2 df-rel 4435 . 2 (Rel ∅ ↔ ∅ ⊆ (V × V))
31, 2mpbir 144 1 Rel ∅
Colors of variables: wff set class
Syntax hints:  Vcvv 2619  wss 2997  c0 3284   × cxp 4426  Rel wrel 4433
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 579  ax-in2 580  ax-io 665  ax-5 1381  ax-7 1382  ax-gen 1383  ax-ie1 1427  ax-ie2 1428  ax-8 1440  ax-10 1441  ax-11 1442  ax-i12 1443  ax-bndl 1444  ax-4 1445  ax-17 1464  ax-i9 1468  ax-ial 1472  ax-i5r 1473  ax-ext 2070
This theorem depends on definitions:  df-bi 115  df-tru 1292  df-nf 1395  df-sb 1693  df-clab 2075  df-cleq 2081  df-clel 2084  df-nfc 2217  df-v 2621  df-dif 2999  df-in 3003  df-ss 3010  df-nul 3285  df-rel 4435
This theorem is referenced by:  reldm0  4642  cnv0  4822  cnveq0  4874  co02  4931  co01  4932  tpos0  6021  0er  6306
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