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Theorem rmobidva 2555
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 1467 . 2  |-  F/ x ph
2 rmobidva.1 . 2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps 
<->  ch ) )
31, 2rmobida 2554 1  |-  ( ph  ->  ( E* x  e.  A  ps  <->  E* x  e.  A  ch )
)
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103    <-> wb 104    e. wcel 1439   E*wrmo 2363
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 1382  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-4 1446  ax-17 1465  ax-ial 1473
This theorem depends on definitions:  df-bi 116  df-nf 1396  df-eu 1952  df-mo 1953  df-rmo 2368
This theorem is referenced by:  rmobidv  2556
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