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

Theorem nrex 2461
Description: Inference adding restricted existential quantifier to negated wff. (Contributed by NM, 16-Oct-2003.)
Hypothesis
Ref Expression
nrex.1  |-  ( x  e.  A  ->  -.  ps )
Assertion
Ref Expression
nrex  |-  -.  E. x  e.  A  ps

Proof of Theorem nrex
StepHypRef Expression
1 nrex.1 . . 3  |-  ( x  e.  A  ->  -.  ps )
21rgen 2424 . 2  |-  A. x  e.  A  -.  ps
3 ralnex 2365 . 2  |-  ( A. x  e.  A  -.  ps 
<->  -.  E. x  e.  A  ps )
42, 3mpbi 143 1  |-  -.  E. x  e.  A  ps
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    e. wcel 1436   A.wral 2355   E.wrex 2356
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-5 1379  ax-gen 1381  ax-ie2 1426
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-fal 1293  df-ral 2360  df-rex 2361
This theorem is referenced by:  rex0  3289  iun0  3771  frec0g  6118  nominpos  8589  sqrt2irr  11066  exmidsbthrlem  11400
  Copyright terms: Public domain W3C validator