ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  rel0 GIF version

Theorem rel0 4520
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 3303 . 2 ∅ ⊆ (V × V)
2 df-rel 4408 . 2 (Rel ∅ ↔ ∅ ⊆ (V × V))
31, 2mpbir 144 1 Rel ∅
Colors of variables: wff set class
Syntax hints:  Vcvv 2612  wss 2984  c0 3269   × cxp 4399  Rel wrel 4406
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 577  ax-in2 578  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2614  df-dif 2986  df-in 2990  df-ss 2997  df-nul 3270  df-rel 4408
This theorem is referenced by:  reldm0  4612  cnv0  4789  cnveq0  4841  co02  4898  co01  4899  tpos0  5971  0er  6256
  Copyright terms: Public domain W3C validator