Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  nel0 Unicode version

Theorem nel0 3415
 Description: From the general negation of membership in , infer that is the empty set. (Contributed by BJ, 6-Oct-2018.)
Hypothesis
Ref Expression
nel0.1
Assertion
Ref Expression
nel0
Distinct variable group:   ,

Proof of Theorem nel0
StepHypRef Expression
1 eq0 3412 . 2
2 nel0.1 . 2
31, 2mpgbir 1433 1
 Colors of variables: wff set class Syntax hints:   wn 3   wceq 1335   wcel 2128  c0 3394 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 604  ax-in2 605  ax-io 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714  df-dif 3104  df-nul 3395 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator