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Theorem rmobidva 2675
Description: Formula-building rule for restricted existential quantifier (deduction form). (Contributed by NM, 16-Jun-2017.)
Hypothesis
Ref Expression
rmobidva.1  |-  ( (
ph  /\  x  e.  A )  ->  ( ps 
<->  ch ) )
Assertion
Ref Expression
rmobidva  |-  ( 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 rmobidva
StepHypRef Expression
1 nfv 1538 . 2  |-  F/ x ph
2 rmobidva.1 . 2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps 
<->  ch ) )
31, 2rmobida 2674 1  |-  ( ph  ->  ( E* x  e.  A  ps  <->  E* x  e.  A  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    <-> wb 105    e. wcel 2158   E*wrmo 2468
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-17 1536  ax-ial 1544
This theorem depends on definitions:  df-bi 117  df-nf 1471  df-eu 2039  df-mo 2040  df-rmo 2473
This theorem is referenced by:  rmobidv  2676
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