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

Theorem moanimv 2018
Description: Introduction of a conjunct into "at most one" quantifier. (Contributed by NM, 23-Mar-1995.)
Assertion
Ref Expression
moanimv  |-  ( E* x ( ph  /\  ps )  <->  ( ph  ->  E* x ps ) )
Distinct variable group:    ph, x
Allowed substitution hint:    ps( x)

Proof of Theorem moanimv
StepHypRef Expression
1 nfv 1462 . 2  |-  F/ x ph
21moanim 2017 1  |-  ( E* x ( ph  /\  ps )  <->  ( ph  ->  E* x ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102    <-> wb 103   E*wmo 1944
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-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-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469
This theorem depends on definitions:  df-bi 115  df-nf 1391  df-sb 1688  df-eu 1946  df-mo 1947
This theorem is referenced by:  mosubt  2778  2reuswapdc  2803  2rmorex  2805  mosubopt  4451  funmo  4967  funcnv  5011  fncnv  5016  isarep2  5037  fnres  5066  fnopabg  5073  fvopab3ig  5298  opabex  5437  fnoprabg  5653  ovidi  5670  ovig  5673  oprabexd  5805  oprabex  5806  th3qcor  6297
  Copyright terms: Public domain W3C validator