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

Theorem mobidv 1936
Description: Formula-building rule for "at most one" quantifier (deduction rule). (Contributed by Mario Carneiro, 7-Oct-2016.)
Hypothesis
Ref Expression
mobidv.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
mobidv  |-  ( ph  ->  ( E* x ps  <->  E* x ch ) )
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    ch( x)

Proof of Theorem mobidv
StepHypRef Expression
1 nfv 1421 . 2  |-  F/ x ph
2 mobidv.1 . 2  |-  ( ph  ->  ( ps  <->  ch )
)
31, 2mobid 1935 1  |-  ( ph  ->  ( E* x ps  <->  E* x ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 98   E*wmo 1901
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-4 1400  ax-17 1419  ax-ial 1427
This theorem depends on definitions:  df-bi 110  df-nf 1350  df-eu 1903  df-mo 1904
This theorem is referenced by:  mobii  1937  mosubopt  4405  dffun6f  4915  funmo  4917  1stconst  5842  2ndconst  5843
  Copyright terms: Public domain W3C validator