ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  mo3 Unicode version

Theorem mo3 2074
Description: Alternate definition of "at most one". Definition of [BellMachover] p. 460, except that definition has the side condition that  y not occur in  ph in place of our hypothesis. (Contributed by NM, 8-Mar-1995.)
Hypothesis
Ref Expression
mo3.1  |-  F/ y
ph
Assertion
Ref Expression
mo3  |-  ( E* x ph  <->  A. x A. y ( ( ph  /\ 
[ y  /  x ] ph )  ->  x  =  y ) )
Distinct variable group:    x, y
Allowed substitution hints:    ph( x, y)

Proof of Theorem mo3
StepHypRef Expression
1 mo3.1 . . 3  |-  F/ y
ph
21nfri 1513 . 2  |-  ( ph  ->  A. y ph )
32mo3h 2073 1  |-  ( E* x ph  <->  A. x A. y ( ( ph  /\ 
[ y  /  x ] ph )  ->  x  =  y ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104   A.wal 1347   F/wnf 1454   [wsb 1756   E*wmo 2021
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-io 705  ax-5 1441  ax-7 1442  ax-gen 1443  ax-ie1 1487  ax-ie2 1488  ax-8 1498  ax-10 1499  ax-11 1500  ax-i12 1501  ax-bndl 1503  ax-4 1504  ax-17 1520  ax-i9 1524  ax-ial 1528  ax-i5r 1529
This theorem depends on definitions:  df-bi 116  df-nf 1455  df-sb 1757  df-eu 2023  df-mo 2024
This theorem is referenced by:  sbmo  2079  rmo3f  2928  rmo3  3047  isarep2  5287
  Copyright terms: Public domain W3C validator