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Theorem rel0 4747
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 3461 . 2 ∅ ⊆ (V × V)
2 df-rel 4629 . 2 (Rel ∅ ↔ ∅ ⊆ (V × V))
31, 2mpbir 146 1 Rel ∅
Colors of variables: wff set class
Syntax hints:  Vcvv 2737  wss 3129  c0 3422   × cxp 4620  Rel wrel 4627
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2739  df-dif 3131  df-in 3135  df-ss 3142  df-nul 3423  df-rel 4629
This theorem is referenced by:  reldm0  4840  cnv0  5027  cnveq0  5080  co02  5137  co01  5138  tpos0  6268  0er  6562
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