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Theorem rel0 4634
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 3371 . 2 ∅ ⊆ (V × V)
2 df-rel 4516 . 2 (Rel ∅ ↔ ∅ ⊆ (V × V))
31, 2mpbir 145 1 Rel ∅
Colors of variables: wff set class
Syntax hints:  Vcvv 2660  wss 3041  c0 3333   × cxp 4507  Rel wrel 4514
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 588  ax-in2 589  ax-io 683  ax-5 1408  ax-7 1409  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-10 1468  ax-11 1469  ax-i12 1470  ax-bndl 1471  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499  ax-i5r 1500  ax-ext 2099
This theorem depends on definitions:  df-bi 116  df-tru 1319  df-nf 1422  df-sb 1721  df-clab 2104  df-cleq 2110  df-clel 2113  df-nfc 2247  df-v 2662  df-dif 3043  df-in 3047  df-ss 3054  df-nul 3334  df-rel 4516
This theorem is referenced by:  reldm0  4727  cnv0  4912  cnveq0  4965  co02  5022  co01  5023  tpos0  6139  0er  6431
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