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Theorem rel0 4489
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 3282 . 2 ∅ ⊆ (V × V)
2 df-rel 4379 . 2 (Rel ∅ ↔ ∅ ⊆ (V × V))
31, 2mpbir 138 1 Rel ∅
Colors of variables: wff set class
Syntax hints:  Vcvv 2574  wss 2944  c0 3251   × cxp 4370  Rel wrel 4377
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 2947  df-in 2951  df-ss 2958  df-nul 3252  df-rel 4379
This theorem is referenced by:  reldm0  4580  cnv0  4754  cnveq0  4804  co02  4861  co01  4862  tpos0  5919  0er  6170
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