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

Theorem nprrel 4412
Description: No proper class is related to anything via any relation. (Contributed by Roy F. Longton, 30-Jul-2005.)
Hypotheses
Ref Expression
nprrel.1  |-  Rel  R
nprrel.2  |-  -.  A  e.  _V
Assertion
Ref Expression
nprrel  |-  -.  A R B

Proof of Theorem nprrel
StepHypRef Expression
1 nprrel.2 . 2  |-  -.  A  e.  _V
2 nprrel.1 . . 3  |-  Rel  R
32brrelexi 4410 . 2  |-  ( A R B  ->  A  e.  _V )
41, 3mto 621 1  |-  -.  A R B
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 1434   _Vcvv 2602   class class class wbr 3793   Rel wrel 4376
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-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064  ax-sep 3904  ax-pow 3956  ax-pr 3972
This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-ral 2354  df-rex 2355  df-v 2604  df-un 2978  df-in 2980  df-ss 2987  df-pw 3392  df-sn 3412  df-pr 3413  df-op 3415  df-br 3794  df-opab 3848  df-xp 4377  df-rel 4378
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator