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

Theorem rmobidv 2577
Description: Formula-building rule for restricted existential quantifier (deduction form). (Contributed by NM, 16-Jun-2017.)
Hypothesis
Ref Expression
rmobidv.1  |-  ( ph  ->  ( ps  <->  ch )
)
Assertion
Ref Expression
rmobidv  |-  ( ph  ->  ( E* x  e.  A  ps  <->  E* x  e.  A  ch )
)
Distinct variable group:    ph, x
Allowed substitution hints:    ps( x)    ch( x)    A( x)

Proof of Theorem rmobidv
StepHypRef Expression
1 rmobidv.1 . . 3  |-  ( ph  ->  ( ps  <->  ch )
)
21adantr 272 . 2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps 
<->  ch ) )
32rmobidva 2576 1  |-  ( ph  ->  ( E* x  e.  A  ps  <->  E* x  e.  A  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    <-> wb 104    e. wcel 1448   E*wrmo 2378
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1391  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-4 1455  ax-17 1474  ax-ial 1482
This theorem depends on definitions:  df-bi 116  df-nf 1405  df-eu 1963  df-mo 1964  df-rmo 2383
This theorem is referenced by:  rmoeqd  2595  disjxp1  6063
  Copyright terms: Public domain W3C validator