ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  rex0 Unicode version

Theorem rex0 3452
Description: Vacuous existential quantification is false. (Contributed by NM, 15-Oct-2003.)
Assertion
Ref Expression
rex0  |-  -.  E. x  e.  (/)  ph

Proof of Theorem rex0
StepHypRef Expression
1 noel 3438 . . 3  |-  -.  x  e.  (/)
21pm2.21i 647 . 2  |-  ( x  e.  (/)  ->  -.  ph )
32nrex 2579 1  |-  -.  E. x  e.  (/)  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    e. wcel 2158   E.wrex 2466   (/)c0 3434
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-fal 1369  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-ral 2470  df-rex 2471  df-v 2751  df-dif 3143  df-nul 3435
This theorem is referenced by:  0iun  3956  finexdc  6916  0ct  7120  exfzdc  10254
  Copyright terms: Public domain W3C validator