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Theorem rmobidva 2907
Description: Formula-building rule for restricted existential quantifier (deduction rule). (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 1678 . 2  |-  F/ x ph
2 rmobidva.1 . 2  |-  ( (
ph  /\  x  e.  A )  ->  ( ps 
<->  ch ) )
31, 2rmobida 2906 1  |-  ( ph  ->  ( E* x  e.  A  ps  <->  E* x  e.  A  ch )
)
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184    /\ wa 369    e. wcel 1761   E*wrmo 2716
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1713  ax-7 1733  ax-12 1797
This theorem depends on definitions:  df-bi 185  df-an 371  df-ex 1592  df-nf 1595  df-eu 2261  df-mo 2262  df-rmo 2721
This theorem is referenced by:  rmobidv  2908  brdom7disj  8694
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