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

Theorem rel0 4632
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 3369 . 2 ∅ ⊆ (V × V)
2 df-rel 4514 . 2 (Rel ∅ ↔ ∅ ⊆ (V × V))
31, 2mpbir 145 1 Rel ∅
Colors of variables: wff set class
Syntax hints:  Vcvv 2658  wss 3039  c0 3331   × cxp 4505  Rel wrel 4512
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 586  ax-in2 587  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-v 2660  df-dif 3041  df-in 3045  df-ss 3052  df-nul 3332  df-rel 4514
This theorem is referenced by:  reldm0  4725  cnv0  4910  cnveq0  4963  co02  5020  co01  5021  tpos0  6137  0er  6429
  Copyright terms: Public domain W3C validator